2003 Math Trails Committee Group Experience · Legare Street - Library Ghost House Mrs. William Heyward, a successful rice planter and sister-in-law of Thomas Heyward, signer of the

2003 Math Trails Committee Group Experience

We came together with a common goal, to develop a collection of original Math Trails for the November conference. The group was comprised of a collection of math instructors from all levels, elementary through college, and one City representative. Some folks knew each other personally and some professionally; others were new faces added for the various talents they possessed. We began our work in earnest on what was perceived as a seemingly easy task. First, locations were scouted and pictures were taken. Soon, location histories were gathered and editing loomed in the horizon. It was at this stage of the game that chocolate began to play an increasingly important role. With red pens sharpened and history books piled high, the group began the diligent task of re-phrasing, researching and shortening the collective mound of text compiled thus far. Dinner became a regular Wednesday night event; Coca-Cola and Hershey’s stock began to soar, and our group of eleven members realized that we were strangers no more. Birthdays were celebrated and weight was lost; and math trails began to emerge from our bits of paper, digital photos, and carefully edited copy. Next, math problems were written, computed, and rechecked. Soon, it was discovered that text had to be added back to some of the location histories that had been previously edited out; text needed to answer the math problems floating just below. Once again, midnight oil was burned, problems rechecked and pictures matched to the trails. Finally, on a cold and windy day, trails were walked and notes were made readying our work for final proofing and printing. Through this process, we all made new friends, and collectively produced a series that winds through our beautiful, historic and haunted city. Enjoy! Math Trails Committee Co-Chairs Ann Long Debby Jeter Members Linda Collie Randal Davis Linda Folk Laura Hoye Judy Long Michelle Long Brenda Morrow Judi Newton Claudia Thomas

Thank you’s and credits Pictures- Debby Jeter, Sandy Powers, Ann Long

Edit- Lillian Warren, Cliff Harris, Laura Amerson, Mark Taylor, Beth Nichols, Judy Covington

Continuous editing – Linda Collie

Website- Conyers Bull and Debby Jeter

CD- Debby Jeter, Tony Shepard, and Clay McCauley

Research Support- Rosemary O’Grady, Dwight Stroud, Joanne Rivers

Flashlights – McDougal Littell – Sherry Bailey

Pencils and water Addison Wesley –Susan Coughlin

Meeting site for the committee- College of Charleston, Trident Technical College

Printing – Trident Technical College

Walking and checking trails:

1. 1.Low Country Math Educators Association 2. Andrea Hazel 3. Pat Teaque 4. Wes Chumley 5. Kinley Alston

City of Charleston – Office of Cultural Affairs and Office of Tourism

Laura Amerson

Randal Davis

SCCTM for financial support

Family and Friends

Bibliography** Coy, Mary Clark. The Civil War Walking History Book. Charleston: 1999.

Hartley, Alan. The Charleston Walking Tour. Charleston: TALK of the TOWNE, 2002.

Leland, Jack. 62 Famous Houses of Charleston, South Carolina. EdWarren Ripley.

Charleston: News and Courier, Evening Post, 1993.

Martin, Margaret Rhett. Charleston Ghosts. Columbia: South Carolina UP, 1992.

Riggs, Bryan. Historic Homes : Charleston, SC. Charleston: Charleston Postcard Co.,1993.

Swann, Nita. The Complete Walking Tour of Historic Charleston. Charleston: Charleston Publishing, 1986.

** Special thanks to the authors of these publications and to the Charleston County Public Library (http://www.ccpl.org) without whose previous efforts this Mathematical Journey Through Charleston would not have been possible.

Original Charleston Math Trails

Take a stroll down charming streets and hidden alleyways that are rich with the history and culture of one of America’s favorite colonial cities! In its heyday, Charleston was called, “Little London,” and shared in a rich coastal heritage that ran the gamut from stately mansions and cotillions to a bustling seaport brimming with pirates. It is the home of Gullah and is awash in the rhymes and rhythms of the islands, a perfect melding of European city and Caribbean culture. The Original Charleston Math Trails will guide you through a maze of the city’s hidden treasures as you solve your way from one landmark to the next. The tour features centuries old architecture and lush southern gardens, with a few surprises along the way. You may even run into one of our dearly departed citizens who can’t seem to solve his way into the great beyond. Solve wisely on your path, as your answers will determine your next move. The questions will be site specific and run from the simple to the complex. Be sure to divide your time and multiply your fun as you follow the links below to the trails.

Copyright 2003 SCCTM Permission for use by teachers with students.

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The Original Charleston Math Trail #1

14 Legare Street - Simmons - Edward’s House A “celibate” husband, a third-story window duelist, and “acorn” post ornaments that turned out to be pinecones or “pineapples,” are part of the history of this house. Francis Simmons, a John’s Island planter, built this house in 1800, but kept his wife at a separate residence. After their wedding he escorted her to the house on Tradd Street. He called regularly, presided at dinner parties and receptions there, but always left just after the final guest departed. The “pinecone” finials resemble pineapples and the gates have been known as the “Pineapples Gates.” In the years 1900 – 1930 this house was the home of Mayor J. Adger Smythe (elected in 1895) and recently it has been the home of Lt. Governor Nancy Stevenson (elected 1978).

1. Evaluate: 2(# of pinecones on gateposts)2 - 1

2. Evaluate: (# of spokes in window over the door)! +1 4!

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Legare Street - Library Ghost House Mrs. William Heyward, a successful rice planter and sister-in-law of Thomas Heyward, signer of the Declaration of Independence, built this house in 1789. Legend says that the ghost of her son, who was fatally shot in a hunting accident, haunts the house. At the hour of his death, his sister reported that she saw him in the library of the house. In later years (1830-1837), Mrs. William Drayton (Mrs. Heyward’s daughter) allowed a school for young girls to operate in the house. In 1870 this house was sold to Augustine Smythe whose descendants still live here.

1. Evaluate: current location +

2. Evaluate: 2 sin(# of this location - # of sisters) + current location (in degrees)

# ghosts

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Legare Street - Sword Gate House The Sword Gates at this house afford an opening through Charleston’s highest garden wall. Legend says the high wall was built to prevent elopements when it was an antebellum home for girls. A 15-year-old daughter of a wealthy Edisto Island planter caught the eye of a New Yorker; however, as a Yankee, he was completely unacceptable to her parents. The young man was ordered to stay away but moved in with a family on a neighboring plantation. The girl’s father took her to Madame Talvandes’ school on Legare Street. On a spring day, she maneuvered her skirts over the fence and eloped. The high walls went up but the wooden gates remained until 1849. George Hopley, who purchased the property in 1849, added the famous Sword Gates. The gates, made by Christopher Werner, had been designed for the Guard House at Broad and Meeting Streets. When Werner made an extra pair, Hopley purchased them for his property. The crossed swords in the design represent authority.

1. Evaluate: (girl's age)2 - 3(# current location) – the digits of the house # reversed.

girl ' sage 2. Evaluate:

∑ i=5

i − 4

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Tradd Street – Stuart House This house was built before 1772 for Colonel John Stuart of the American Revolution. It is a 3 and ½ story wooden home with a “captain’s walk” or “widow’s walk” on the top story. Colonel Stuart was the Royal Commissioner of Indian Affairs for an area stretching from Virginia to Florida. Because he remained loyal to England, his house was confiscated by Patriot authorities and quartered a Patriot officer. Tradition says that General Francis Marion (a teetotaler) attended a party here and was forced to leap from a window to escape the drunken host who refused to let his guests leave until they were drunk. General Marion broke his leg from the fall and was recuperating at his plantation, thus avoiding capture when the British seized Charleston in 1780.

1. Evaluate: 15(the # of years the house stood before the British seized Charleston)

10

22

2. Evaluate: [2(# of isosceles Δ on street entry side)2 + ∫ dx ] ÷ 10 0

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Orange Street – Jonathan Badger Tenement Jonathan Badger, a Charleston cabinetmaker is credited with the construction of this 3-story Georgian style house in 1775. The original house consisted of 2 bays and a central stairway. In the 19th century a dining room was added and it was not until the early 20th century that the original 2-story brick outbuilding was attached to the main house. Alexander Petrie developed Orange Street in the 1760’s on property that was once Dr. Samuel Carnes orange garden. This street is considered a rare surviving example of a late colonial period residential development. Many of the original structures still remain.

1. Assign the letters of the alphabet to numbers: A = 1, B = 2, C = 3, etc. Determine the sum in the street name Orange and then multiply by 2.

2. Using the letters in the street’s name, determine the probability of choosing a vowel

from the six letters. Multiply that result by 2 dozen and then again by 10.

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Broad Street – Cathedral of St. John The Right Reverend John England, Bishop of Charleston for the Roman Catholic Church, built a simple wooden chapel on this property, which he purchased in 1821. England was the first bishop of the Diocese that included approximately 1000 Catholics in South Carolina, North Carolina and Georgia. A larger Cathedral was built on the site between the years 1850-1854, but was destroyed by the Great Fire of 1861. Sadly, the fire insurance on the Cathedral had lapsed. For many years the congregation worshipped elsewhere, until 1890 when the present Cathedral was started with a bequest of nearly $50,000 from John McKeegan. A company from Munich, Germany made the stained glass and the design was patterned after German Gothic churches of the 14th century.

1. Evaluate: house # current location - (year of Great Fire - year the property was

purchased)

2. Let s = # of semicircular “humps” on the isosceles triangle legs over door Let c = # cross designs near circular window Let p = sections in circular window Let w = all windows over main entry

Evaluate: sc - p2 (w - c)

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Meeting Street - St. Michael’s Episcopal Church This is the oldest church structure in Charleston representing God’s Law on the southeast corner on the four corners of law. It is one of the most important 18th century Colonial Georgian buildings in the nation. The builder, Samuel Cardy, laid the cornerstone on February 17, 1752 and the church was opened for services on February 1, 1761. Tiffany windows were installed in 1906. The clock, one of few existing Aynsworth Twaites in the world, along with the ring of eight brass bells, was imported from England in 1764. The bells have crossed the Atlantic five times. They were returned to England as spoils of the Revolutionary War, bought by a London merchant and shipped back to Charleston. Then in an attempt at safekeeping, the bells were shipped to Columbia during the Civil War, but were damaged by the fire there and then shipped back to England for recasting. The tower of St. Michael’s served as a Colonial lighthouse, an observation tower in the Revolution, a signal post in the Civil War, and as an air raid siren station during World War II. The original box pews, which were rented to church families, still remain. Pew # 43 was reserved for visiting dignitaries such as George Washington, the Marquis de Lafayette, and Robert E. Lee.

1. To the current house number add the product of the number of times the bells crossed the Atlantic and the number of years between laying the cornerstone and the first service, then subtract 10.

6

2. Evaluate: 10(# sides in the geometric shape of the upper levels of steeple) + ∫ 2x dx 1

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Meeting Street – Mills House Hotel The Mills House Hotel is an Italianate structure modeled after the original built about 1853. It stands on the site of the original Mills House Hotel. The hotel cost $200,000 to build, was 5 stories tall, and contained 125 rooms. It is said that Gen. Robert E. Lee stood on its iron balcony as he watched the great fire of 1861 sweep through Charleston, destroying approximately 500 buildings. The staff of the hotel was able to save it by hanging wet blankets from the hotel windows. During the Civil War, General P. G. T. Beauregard used the hotel as his headquarters until Otis Mills offered his own residence on Meeting Street. The present building was reconstructed in 1968 using the original ironwork and in the same Italianate style.

1. Evaluate: # of buildings destroyed ÷ 5 + (10)(5)

2. Let b = # of balcony doors and a = # of stone arches at entry. Evaluate: date built – [1000 + ba] + arcsin ½ - 4

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Meeting Street – Circular Church English Congregationalists, Scottish and Irish Presbyterians, and French Huguenots of the original settlement of Charles Town founded this congregation, known as the Independent Church, around 1681. Their second meeting house was built at 150 Meeting Street in 1732. About 1805, that hall was replaced by a circular structure, designed by architect Robert Mills, a Charleston native. The present church was named for Mills’s earlier church, which burned in 1861. The building is not really circular, but triapsidal (conjoining of circles and/or arches) much like the 11th century Church of the Apostle in Cologne. Designed by architects Stevenson and Green, the Romanesque church was constructed as the city was rebuilding after the 1886 earthquake, using brick from the earlier structure. The church is an excellent example of Romanesque style in its broad roof plane, ribbons of windows, short tower, and large arched entry. The graveyard is the city's oldest burial ground, with one monument remaining from the 17th century. Today's congregation is United Presbyterian Church, USA.

1. Determine the sum: current house # + 1/5(current house number) + 22.

2. Evaluate: (# of degrees in a circle)/12 + 5(# of degrees in a semicircle)/6+ 82/3

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Meeting Street – Market Hall The Market Hall, a National Historic Landmark, was designed by local architect Edward Brickell White and is considered an excellent example of Roman Revival architecture. The stairways are ornate with ironwork, and Tuscan columns support the massive portico. The site of the Market Hall was donated to the city by the Pinckney family with the stipulation that ownership revert to the family should the land be used for any purpose other than a city market. Meat and produce were brought to the market from nearby rural producers. In the past a meat market could be located by the presence of buzzards (Charleston eagles), which scavenged for leftovers at the end of the day. However, the stucco frieze is decorated with sheep and bull skulls, which also identifies this as a meat market. The arcaded basement of Market Hall houses various shops and an eatery, while the second floor houses a museum. The sheds behind the Market Hall continue to be used as a market place for individual vendors who sell a variety of Lowcountry crafts and produce.

1. Evaluate: 5(total # of steps leading to portico)

2. Let x = # of complete columns supporting front of portico. Evaluate: f(x) = x4 – x3 – x2

f ′(x)

given

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East Bay Street – Custom House With funds appropriated by Congress in 1848, the site of Fitzsimons’ Wharf was bought in 1849 to build the US Custom House. During excavation of the basement, the remains of Craven’s Bastion, a colonial-era fortification, were found. The building’s construction, interrupted by the Civil War, was completed in 1879 as it is today. Marble was used for the two upper floors. Roman Corinthian porticos, engaged columns, and entablature (the section that lies between the columns and the roof) surround the cruciform (shaped like a cross) building. Emile T. Viett carved the marble capitals and decorative work.

Congratulations! You have completed your Math Trail. We hope that you were able to

work the problems, learn some history and most of all had fun doing math with friends.

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ANSWER KEY

Trail #1 14, 31, 32, 106, 12, 120, 80, 115, 150, 184, 200 Trail #1 14 Legare Street – Edward’s House 31 Legare Street – Library Ghost 32 Legare Street – Sword Gate House 106 Tradd Street – Stuart House 12 Orange Street – Jonathan Badger Tenement 120 Broad Street – Cathedral of St. John 80 Meeting Street – St. Michael’s Episcopal Church 115 Meeting Street – Mills House Hotel 150 Meeting Street – Circular Church 184 Meeting Street – Market Hall 200 East Bay Street – Custom House

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31 Legare St. - Library Ghost House Mrs. William Heyward, a successful rice planter and sister-in-law of Thomas Heyward, signer of the Declaration of Independence, built this house in 1789. Legend says that the ghost of her son, who was fatally shot in a hunting accident, haunts the house. At the hour of his death, his sister reported that she saw him in the library of the house. In later years (1830-1837), Mrs. William Drayton (Mrs. Heyward’s daughter) allowed a school for young girls to operate in the house. In 1870 this house was sold to Augustine Smthye whose descendants still live here.

1. Add 7 to the sum of the digits in the date this house was built.

2. Evaluate: 2 sin [(# of current location)º - (# of sisters)º] + # of current location

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Legare Street - Sword Gate House The Sword Gates at this house afford an opening through Charleston’s highest garden wall. Legend says the high wall was built to prevent elopements when it was an antebellum home for girls. A 15-year-old daughter of a wealthy Edisto Island planter caught the eye of a New Yorker; however, as a Yankee, he was completely unacceptable to her parents. The young man was ordered to stay away but moved in with a family on a neighboring plantation. The girl’s father took her to Madame Talvandes’ school on Legare Street. On a spring day, she maneuvered her skirts over the fence and eloped. The high walls went up but the wooden gates remained until 1849. George Hopley, who purchased the property in 1849, added the famous Sword Gates. The gates, made by Christopher Werner, had been designed for the Guard House at Broad and Meeting Streets. When Werner made an extra pair, Hopley purchased them for his property. The crossed swords in the design represent authority.

1. Multiply the bride’s age by 10, then subtract 1 less than 3 times her age.

2. Evaluate: (girl’s age)2 – 3(# current location) - digits of the current location

reversed.

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Tradd Street - Stuart House This house was built before 1772 for Colonel John Stuart of the American Revolution. It is a 3 and ½ story wooden home with a “captain’s walk” or “widow’s walk” on the top story. Colonel Stuart was the Royal Commissioner of Indian Affairs for an area stretching from Virginia to Florida. Because he remained loyal to England, his house was confiscated by Patriot authorities and quartered a Patriot officer. Tradition says that General Francis Marion (a teetotaler) attended a party here and was forced to leap from a window to escape the drunken host who refused to let his guests leave until they were drunk. General Marion broke his leg from the fall and was recuperating at his plantation, thus avoiding capture when the British seized Charleston in 1780.

1. Let x = # of stories in the house and let y = sum of the digits in the year the house was

built. Evaluate: 2xy +1

10

2. As General Marion leaped from the balcony, his path took the shape of a parabola with the equation f(x) = -6x2 + 10. Find the coefficient of x in the negation of f′(x).

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Orange Street – Jonathan Badger Tenement Jonathan Badger, a Charleston cabinetmaker is credited with the construction of this 3-story Georgian style house in 1775. The original house consisted of 2 bays and a central stairway. In the 19th century a dining room was added and it was not until the early 20th century when the original 2-story brick out building was attached to the main house. Alexander Petrie developed Orange Street in the 1760’s on property that was once Dr. Samuel Carnes orange garden. This street is considered a rare surviving example of a late colonial period residential development. Many of the original structures still remain.

1. Assign the letters of the alphabet to numbers, for example A = 1, B = 2, etc. Determine the sum of the letters in the street name and multiply by 2.

2. Let n = the probability of choosing a vowel from the letters in the street’s name and let

m = # of arrangements of the letters in the street’s name. Evaluate the product of m and n, then divide the result by 3.

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Broad Street - Cathedral of St. John The Right Reverend John England, Bishop of Charleston for the Roman Catholic Church, built a simple wooden chapel on this property, which he purchased in 1821. England was the first bishop of the Diocese that included approximately 1000 Catholics in South Carolina, North Carolina and Georgia. A larger Cathedral was built on the site between the years 1850-1854, but was destroyed by the Great Fire of 1861. Sadly the fire insurance on the Cathedral had lapsed. For many years the congregation worshipped elsewhere, until 1890 when the present Cathedral was started with a bequest of nearly $50,000 from John McKeegan. A company from Munich, Germany made the stained glass and the design was patterned after German Gothic churches of the 14th century.

1. Evaluate: current street # 4 # of windows above the main door

2. Let n = # of windows above the main door. n

Evaluate: ∫3x 2 − 2x dx - 100 0

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1. The steeple of this church is made of five parts with the three middle parts having the same geometric shape. Evaluate: (# of columns)(# of sides on the three middle parts) + 2(# of columns) + # of steeples.

2. The steeple of this church is made of five parts with the three middle parts having the

same geometric shape. Find the central angle of a cross section of any one of these three parts and add it to the measure of one angle in an equiangular triangle.

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Meeting Street - Hibernian Hall Hibernian Hall was built in 1839 for $40,000 from the designs of a Philadelphia architect, Thomas U. Walter, who is best known for adding the great dome to the U.S. Capitol Building. The original portico collapsed in the earthquake of 1886 and was rebuilt in more elaborate form. The Irish harp is contained in the panel above the door as well as the overthrow of the iron gates. The ironwork design is attributed to Christopher Werner of Charleston. The Hibernian Society was formed in 1801 as an Irish Benevolent Society. Presidents of the society alternate between Catholic and Protestant, and membership is passed only from father to son. In early 1861, the state legislature temporarily moved to Charleston and met in Hibernian Hall. During this stay they adopted the state flag that has since been used in South Carolina. Of all the social functions held in Hibernian Hall, the St. Cecilia’s Society Ball is still the most famous.

1. Evaluate: 3(year hall built - year society formed) + 2

2. The Irish harp above the door appears to be made of gold. Solve this equation to

determine a possible weight in ounces of the “gold” Irish harp. x2 – 113x –348 = 0.

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Meeting Street - Old Lower Fire Station Built in 1887, the Flemish-bonded brick structure was completed at a cost of $7,000 as a strategic move to strengthen the City’s central fire warning system. The tower at the rear of the property contains a 2,500-pound iron bell. The bell was used for everything from alerting citizens to fire and hurricanes to notifying the public about important national events, and until 1927, as a means to tell time by tolling daily at 12:00 Noon. The Old Lower Fire Station has been converted to city offices; however, it remained active as a fire station, keeping watch over its citizens, until 1953. Today, the bell is silent except when used ceremonially. It most recently rang 343 times, once for each firefighter lost in the September 11th World Trade Center tragedy.

1. Evaluate: present address minus 3, added to 2(day last commemorated by the bell)

2. Consider a semicircle like the ones above the large windows on the ground level. -1 − 2

If this semicircle represents the unit circle from 0˚ to 180˚, find the cos 2

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Church Street - Dock Street Theatre The Dock Street Theatre is located in the shell of the old Planter’s Hotel which was famous food as well as being the birthplace of Planter’s Punch. In 1838 an infamous guest of the hotel, Junius Brutus Booth allegedly attempted to murder his manager in one of the hotel’s rooms. The original Dock Street Theatre, which was the first building built specifically for theatrical performances in America, raised its curtain February 12, 1736 with a production of The Recruiting Officer. In 1935, the City of Charleston, as a Works Progress Administration project, remodeled the old Planter’s Hotel property as the new Dock Street Theatre. Dorothy and DuBose Heyward were in attendance when the Theatre reopened on November 26, 1936 with a repeat performance of The Recruiting Officer, photos of which ran in the newly established Life magazine. The plaster in the Theatre predates construction (1806) and was salvaged from the Ratcliffe-King House slated for demolition farther up the street.

1. Write the date the Theatre reopened as 11/26/1936. Add the digits in the date, multiply by 5 and add 1.

2. The Dock Street Theatre is still a working theatre and must sell tickets in order to

exist. If students are charged $12, adults are charged $15, and 200 tickets are sold for a total of $2838, how many adult tickets were sold?

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Church Street - St. Philip’s Church The “Mother Church of the Colony,” organized in 1680, is the oldest congregation in the city. Legend says that the first minister, in an inebriated condition, was accused of christening a young bear in 1682. The congregation moved to this site in 1722, a building hailed as “…unsurpassed in architectural beauty by any edifice in the union.” The church caught fire in 1796, but was saved by a black boatman who ripped burning shingles from the roof. As a reward, he was given his freedom. The church caught fire again in 1835 and this time it was burned to the ground. Reconstruction began immediately, incorporating many of the original building’s features, notably the triple Tuscan portico. The church has two cemeteries; the one closest to the church is reserved for those folks lucky enough to be born in Charleston. Even the great Vice-President, John C. Calhoun, could not be buried on the “local” side due to his place of birth.

1. Find the congregation’s age at the time of the fire in 1835 then add the number formed by the tens and ones digits of the year it burned.

2. Find the area of the space in the front door between the inset squares and rectangles if

the door is 12 feet by 4 feet, the area of each square is 292.7 square inches and the area of each rectangle is 400 square inches. Round your answer to the nearest whole number.

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Answer Key

Trail #2 31, 32, 106, 12, 120, 80, 105, 116, 135, 146, 200 Trail #2 31 Legare Street – Library Ghost 32 Legare Street – Sword Gate House 106 Tradd Street – Stuart House 12 Orange Street – Jonathan Badger Tenement 120 Broad Street – Cathedral of St. John 80 Meeting Street – St. Michael’s Episcopal Church 105 Meeting Street – Hibernian Hall 116 Meeting Street – Old Lower Fire Station 135 Church Street – Dock Street Theatre 146 Church Street – St. Philip’s Church 200 East Bay Street – Custom House


21 King Street - O’Donnell House This house is known as “O’Donnell’s Folly.” O’Donnell set out to build a house for his bride-to- be that would stand out in an area of outstanding houses. The residence took so long to build that his fiancée married someone else, leaving him with a tall house and many bedrooms, but no wife to help fill them. O’Donnell lived there until his death in 1882 and died a bachelor. He left his estate to Father Tom Burke of the Order of St. Dominick to be used for the good of the poor of his native Galway.

1. What is the one’s digit in the year that O’Donnell died?

2. Let n = the number of O’Donnell’s wives. Evaluate: ∑ (i2 − i) i=n

2

Ladson Street – John Drayton House This site was the home of John Drayton, which was given to him in 1746 by his father-in-law, Lt. Gov. William Bull. Ladson Street existed to provide access between the Drayton and Bull family homes. John Drayton’s home has been remodeled several times over the years to include the semi-circular bay on the west side and the Colonial Revival façade.

Photo courtesy of Charleston County Public Library Website

1. Find the product of 5 and the number of letters in John Drayton less 4.

2. Using degrees, solve for x:

ln(number of columns at entrance) = ln x + ln(1 -

arcsin

x

2 / 2)

Meeting Street - Nathaniel Russell House Nathaniel Russell was a Northern expatriate who engaged in the import-export business. He was one of the wealthiest men at the time. Legend holds that this mansion was built to be a beautiful backdrop for his two available, but less than attractive, daughters. If true, this ploy was successful. This mansion faces the street, a departure from the single house style popular in Charleston. It is well known for its "flying" staircase and second story balconies. The exterior is a study in contrasts using two kinds of brick, wrought iron, wood, and marble. Today, the Historic Charleston Foundation operates this house as a museum.

1. Find the product of the number of Nathaniel Russell’s daughters and 25. To this product add the number of windows with balconies for his daughters to be displayed.

2. Let n = the number of windows on the front of the house, facing the street and

n m+2

let m = number of red arches, then evaluate: ∫ (2x − 2)dx + ∫ dx 0 0

4

Meeting Street - First Scots Presbyterian Church In 1731, twelve Scottish families withdrew from the Independent or Congregational Church and founded the “Scots Kirk” or Scotch Meeting. The original frame building was replaced in 1814 by the present one. It is the fifth oldest church in the city and unique with its two towers. The seal of the Church of Scotland is in the window over the main entrance. The Church bell was given to the Confederacy in 1863 to be melted down for use as ammunition and was not replaced until May 1999.

1. Add 7 to the year that the 12 Scottish families left the Congregational Church then

subtract this sum from the year the present church was built.

2. If f(x) = ln x, evaluate f ' 1 ⋅ (century when the church bell was melted down)

Meeting Street - Judge Elihu Hall Bay House This home once belonged to a beloved Charleston judge who purchased the house in 1784. Less than two years later, he found himself sharing his home with a collection of spirits trapped there through a series of poor choices. Late on a dark August night in 1786, Judge Bay awoke to the sound of drunken men just outside his windows on St. Michael’s Alley. Suddenly, two foolish young men, who in their inebriated state decided to settle differences with a duel, fired shots. The judge threw open his windows in time to see six friends carrying a wounded body up his front stairs with the intention of leaving the dying man in the judge’s care. The unfortunate young man died in the upstairs front bedroom as a result of his injuries. Over the next century on calm nights, footsteps of six friends could be heard on the stairs carrying their dying friend to a soft bed. All were bound there, sentenced to relive that hot August night for an eternity. Relief came in 1942 when St. Michael’s Church purchased the house for use as its rectory. Since that time, the footsteps have ceased their hurried ascent upstairs.

1. Evaluate: the number of stories in this house squared times the number of letters in “Judge Elihu,” less one.

2. Determine the smallest of 3 consecutive integers such that the sum of the integers

equals the product of the number of floors of this house times the number of windows facing the street times 15.

Church Street – Cabbage Row Cabbage Row was named for the buildings along Church Street where vegetable farmers would come to display their goods for sale. This valuable three story double tenement of stuccoed brick was called "Cabbage Row" because black tenants there put cabbages for sale on the windowsills. This was partly the inspiration for "Catfish Row," the locale of DuBose Heyward's novel Porgy. A notable feature is the wrought iron grille in the entrance to the central arched passage.

1. Find the product: (# of windows on both houses – 1)(# of shutters on both houses + 2).

2. Given that the derivative of a cabbage is a brussel sprout, find 12

∫ 2(brussel sprout)(cabbage) d(cabbage) 3

Church Street - Dock Street Theatre The Dock Street Theatre is located in the shell of the old Planter’s Hotel which was famous food as well as being the birthplace of Planter’s Punch. In 1838 an infamous guest of the hotel, Junius Brutus Booth allegedly attempted to murder his manager in one of the hotel’s rooms. The original Dock Street Theatre, which was the first building built specifically for theatrical performances in America, raised its curtain February 12, 1736 with a production of The Recruiting Officer. In 1935, the City of Charleston, as a Works Progress Administration project, remodeled the old Planter’s Hotel property as the new Dock Street Theatre. Dorothy and DuBose Heyward were in attendance when the Theatre reopened on November 26, 1936 with a repeat performance of The Recruiting Officer, photos of which ran in the newly established Life magazine. The plaster in the Theatre predates construction (1806) and was salvaged from the Ratcliffe-King House slated for demolition farther up the street.

1. Form a new 3-digit number using the digits in the year the theatre was re-opened The thousands digit the tens digit the ones digit .

x 4

2. Given f(x) =

, find: (the year the Theatre reopened) – (the year the Theatre 4

raised its curtain) – f ′ (# of arches on the balcony – 1)

Church Street - French Huguenot Church Today the church stands as the first and last French Protestant congregation in America. The present building is Charleston’s first example of Gothic Revival architecture and was completed at a cost of $12,000. On the exterior, ornamentation such as buttresses and lancet windows can be evidenced, while inside, the railed chancel can be seen beneath the original 1847 Henry Erben organ. The church was called the Church of the Tides due to the fact the Dock Street (now Queen Street) was originally a tidal creek.

1. If the present building were to be paid for by only 82 members, how much would it have cost each of them to the nearest dollar?

2. Suppose the roof of the church is an isosceles triangle with the top vertex angle equal

to 112o . Find the measure of the exterior angle x shown below.

x

Church Street - St. Philip’s Church The “Mother Church of the Colony,” organized in 1680, is the oldest congregation in the city. Legend says that the first minister, in an inebriated condition, was accused of christening a young bear in 1682. The congregation moved to this site in 1722, a building hailed as “…unsurpassed in architectural beauty by any edifice in the union.” The church caught fire in 1796, but was saved by a black boatman who ripped burning shingles from the roof. As a reward, he was given his freedom. The church caught fire again in 1835 and this time it was burned to the ground. Reconstruction began immediately, incorporating many of the original building’s features, notably the triple Tuscan portico. The church has two cemeteries; the one closest to the church is reserved for those folks lucky enough to be born in Charleston. Even the great Vice-President, John C. Calhoun, could not be buried on the “local” side due to his place of birth.

1. Above each section of 4 columns there is a triangular section of the roof. Subtract 101 from the number of degrees in a triangle.

2. Let n = number of sectors in the doorway arch. Evaluate: n − 1

1 6

Cumberland - Powder Magazine A National Historic Landmark, the Powder Magazine is the oldest public building in South Carolina. Defense of the colony was a priority. To that end, fortified walls were constructed around the city. The Powder Magazine was built with brick walls 32 inches thick in 1713 to store the city's gunpowder. The interior roof structures were constructed so that the building would implode if an explosion were to occur inside. The steeply tiled roof, which was typical in that era, is gabled on all sides. The building has undergone an extensive archaeological and architectural conservation project, led by the Historic Charleston Foundation.

1. Convert the thickness of the brick walls in inches to feet. Truncate the fraction or decimal, then multiply by the number of years in 10 decades.

2. If the “peak” of the roof directly above the entrance is represented by the equation

y = - x + (age of building - 90). Determine the absolute maximum of the “peak.”



work the problems, learn some history, and most of all, had fun doing math with friends.

Answer Key

Trail #3 21, 2, 51, 53, 76, 89-91, 135, 136, 146, 79, 200 Trail #3 21 King Street – O’Donnell House 2 Ladson – John Drayton House 51 Meeting Street – Nathaniel Russell House 53 Meeting Street – First Scots Presbyterian Church 76 Meeting Street – Judge Elihu Hall Bay House 89-91 Church Street – Cabbage Row 135 Church Street – Dock Street Theatre 136 Church Street – French Huguenot Church 146 Church Street – St. Philip’s Church 79 Cumberland – Powder Magazine 200 East Bay Street – Custom House

Original Charleston Math Trail #4

2 Ladson Street – John Drayton House This site was the home of John Drayton, which was given to him in 1746 by his father-in-law, Lt. Gov. William Bull. Ladson Street existed to provide access between the Drayton and Bull family homes. John Drayton’s home has been remodeled several times over the years to include the semi-circular bay on the west side and the Colonial Revival façade.


1. Begin with the year in which the home was given to John Drayton and subtract 1723. Take your answer and write the next two odd integers.

2. The sum of 3 consecutive odd integers is equal to the measure of the top vertex angle

of the isosceles triangular window at the top of the house. Assuming the base angles of the triangle are 52 degrees 30 minutes, determine the 3 consecutive odd integers.

, , Meeting Street. - The Three Sisters’ Houses These houses are a group of Charleston single houses, built by a father to attract potential suitors for each of his three daughters. True to single house fashion, each house has one end that faces the street. All are three-story dwellings, have wrought iron balconies overlooking the street, and pretty gardens viewable through wrought iron gates. Albert Delmar is credited with building 23 Meeting Street around 1750. The molding above the top windows is often referred to as the “eyebrows” of this house. The first of the trio, 25 Meeting Street, was built while Charleston was still a colony. The second, 27 Meeting Street, has a basement that raises the first floor higher than the other two houses and has a hip roof. This last house was constructed after the Revolutionary War.

1. Multiply the number of sisters by half a dozen.

2. Find the sum of the degrees of the three similar figures on the gates to this house.

Now divide by the measure of one interior angle of an equilateral triangle.

Meeting Street - Thomas Heyward House The Thomas Heyward house was built around the year 1803. It is unclear whether Nathaniel Heyward or his brother Thomas Heyward, a signer of the Declaration of Independence, built this three-story home. There is a secret room on the second floor that was used to store wine. James Adger, who operated the first coastal steamship line in the United States, lived in this home at one time.


1. Take the number of stories in this house and multiply that number by the number of letters in the word Independence. Take your product and add one to it.

2. Let n = the number of Norman doors facing the street.

6

Evaluate: ∫ 2x dx + 1 n−1

n

Meeting Street – Otis Mills House This house was built between the years of 1775 –1782. In 1809 William Brisbane, a planter, bought the home and later added the large bays on the front of the house. The next owner of this house was Otis Mills, who bought the house in 1848. In October 1862, Mr. Mills loaned the house to General Pierre G.T. Beauregard, who remained at the house until August 1863.

circular openings

1. Take the year in which General Beauregard moved out and subtract the year in which Mr. Mills bought the house. Multiply that difference by three.

2. Let n = ½ the number of circular openings under the bottom windows.

Evaluate: arcsin( 1 )

Meeting Street - Philip Simmons Iron Work A local French Huguenot family, the Chazals, built this Victorian gem in 1889. Dr. Chazal was a participating doctor at the local Medical College. The mansion remained in the Chazal family until 1966 when it was sold to the present owner who began an extensive restoration project. The original portico was removed and double wooden front doors with folding screens were added, as was the rounded brick terrace. The original transom was moved to become the front basement window, now visible at the lower left side of the building. It was also at this time that the local legendary blacksmith, Philip Simmons, was commissioned to design the new ironwork for the house. Mr. Simmons, born on June 9, 1912 on Daniel Island, is responsible for much of the ironwork added to Charleston structures and public buildings in the twentieth century. The pattern he developed for this home incorporates scrolls and hearts for the front gate, fencing, terrace portico, and lower level window grilles. The upstairs window grilles are a mixture of geometrical patterns including circles and rounded rectangles.

1. Begin with the year the Chazal’s sold the mansion, subtract the year of Mr. Simmons’ birth, add 5.

2. Determine x and y given: log7 x = ½ the number of “teardrops on the gate, and

logy (# of teardrops on gate + # of hearts on gate + 2) = 1. Evaluate: x + y

Meeting Street - The Branford -Horry House This home was built by merchant Benjamin Savage around 1750. His niece, Elizabeth, and her husband, William Branford, inherited the house. Elias Horry, Mr. Branford’s grandson, added the double piazzas over Meeting Street in 1830. The parlor for this home is located on the second floor to avoid dust and noise from the street.

1. Take year in which the house was built and subtract it from the year in which Mr. Horry added the double piazzas.

2. Let n = the number of all columns on the 2nd floor. Evaluate: n ⋅ log 1024 2


1. Take the number of times the bells crossed the Atlantic and multiply this number with the prime numbers preceding and following it.

2. Determine the degree measure of one interior angle of a cross section of the bell

tower and then subtract arcsin(1/2).

Meeting Street - Hibernian Hall Hibernian Hall was built in 1839 for $40,000 from the designs of a Philadelphia architect, Thomas U. Walter, who is best known for adding the great dome to the U.S. Capitol Building. The original portico collapsed in the earthquake of 1886 and was rebuilt in more elaborate form. The Irish harp is contained in the panel above the door as well as the overthrow of the iron gates. The ironwork design is attributed to Christopher Werner of Charleston. The Hibernian Society was formed in 1801 as an Irish Benevolent Society. Presidents of the society alternate between Catholic and Protestant, and membership is passed only from father to son. In early 1861, the state legislature temporarily moved to Charleston and met in Hibernian Hall. During this stay they adopted the state flag that has since been used in South Carolina. Of all the social functions held in Hibernian Hall, the St. Cecilia’s Society Ball is still the most famous.

1. Take the amount for which this building was built and divide by 1000. Multiply this

number by 3, then subtract 4 from that product.

2. Let n = number of columns + 1. Evaluate: 2n – 2(n - 1)


1. Solve for n: n + 159 = number of times bell rang for September 11

2. Let x = number of semicircular arches above the windows and doors on the ground floor, street side. Evaluate: x3 – x2 + x – 2

Meeting Street – Market Hall The Market Hall, a National Historic Landmark, was designed by local architect Edward Brickell White and is considered an excellent example of Roman Revival architecture. The stairways are ornate with ironwork, and Tuscan columns support the massive portico. The site of the Market Hall was donated to the city by the Pinckney family with the stipulation that ownership revert to the family should the land be used for any purpose other than a city market. Meat and produce were brought to the market from nearby rural producers. In the past a meat market could be located by the presence of buzzards (Charleston eagles), which scavenged for leftovers at the end of the day. However, the stucco frieze is decorated with sheep and bull skulls, which also identifies this as a meat market. The arcaded basement of Market Hall houses various shops and an eatery, while the second floor houses a museum. The sheds behind the Market Hall continue to be used as a market place for individual vendors who sell a variety of Lowcountry crafts and produce.

1. Evaluate: 5(total # of steps leading to portico)

2. Let x = # of complete columns supporting front of portico. Evaluate: f(x) = x4 – x3 – x

f ′(x)

given




Answer Key

Trail #4 2, 23-25-27, 18, 37, 45, 59, 80, 105, 116, 184, 200 Trail #4 2 Ladson Street – John Drayton House 23, 25, 27 Meeting Street – The Three Sisters’ Houses 18 Meeting Street – Thomas Heyward House 37 Meeting Street – Otis Mills House 45 Meeting Street – Philip Simmons Iron Work 59 Meeting Street – The Branford-Horry House 80 Meeting Street – St. Michael’s Episcopal Church 105 Meeting Street – Hibernian Hall 116 Meeting Street – Old Lower Fire Station 184 Meeting Street – Market Hall 200 East Bay Street – Custom House


2 Meeting Street Inn Mr. Waring P. Carrington acquired the site for this home in 1889, however construction did not begin until 1890. It was upon the occasion of his marriage to Martha Williams (daughter of George Walton Williams of the Calhoun Mansion) that Mr. Carrington’s father-in-law gave the couple the vast sum of $75,000 with which to build their first residence. For their fifth wedding anniversary, Mr. Carrington purchased two beautiful Tiffany floor-to-ceiling stained-glass panels, which are still part of the home today and can be seen in the first-floor sitting area of the Inn. This Queen Anne style gem affords one of the most spectacular views of White Point Gardens and the Charleston harbor in the city.

1. Find the sum of the street number of this house and the number of floor to ceiling Tiffany stained glass panels in this home. Then square that number.

2. If the radius of the arches across the porch is 8 ft., the distance between the

supporting pillars is the same as the next address on Meeting Street.

Meeting Street- Calhoun Mansion When construction was completed in 1876 at a cost of $200,000 (quite a considerable sum of money in that time), an article in the News and Courier hailed the home as, “the handsomest and most complete private residence in the South.” Spanning some 24,000 square feet, the home is considered the largest single-family residence in the city. The style incorporates Italianate and Renaissance Revival styles. The structure features sweeping piazzas; walnut, oak and kingwood woodwork; fireplace and floor tiles by the Minton China Company; and a crystal ceiling in the second floor music room. Augusta, Georgia merchant George Walton Williams built this home. His daughter later married the grandson of Vice-President John C. Calhoun.

1. Take the area of the floor space in this large home and divide it by 1000. Then subtract half of the floor number for the location of the crystal ceiling music room.

2. Above each window is a segment of a circle. Assume that the radius of this circle is

9 feet and the central angle of the sector is 90º. Using π =

segment. Round your answer to the nearest integer.

22 , find the area of the 7

, , Meeting Street – Three Sisters’ Houses These houses are a group of Charleston single houses, built by a father to attract potential suitors for each of his three daughters. True to single house fashion, each house has one end that faces the street. All are three-story dwellings, have wrought iron balconies overlooking the street, and pretty gardens viewable through wrought iron gates. Albert Delmar is credited with building 23 Meeting Street around 1750. The molding above the top windows is often referred to as the “eyebrows” of this house. The first of the trio, 25 Meeting Street, was built while Charleston was still a colony. The second, 27 Meeting Street, has a basement that raises the first floor higher than the other two houses and has a hip roof. This last house was constructed after the Revolutionary War.

1. In the building date for the first house, add the digits in the thousands and hundreds places together. Then multiply by the digit in the tens place. Finally, add the sum of the digits in the street number.

2. If the area of one of the circles in the gate is 64 square inches, let r = the radius of

the circle. Find the measure of a central angle in a sector of a circle that is divided into r sectors.

Meeting Street - Philip Simmons Iron Work A local French Huguenot family, the Chazals, built this Victorian gem in 1889. Dr. Chazal was a participating doctor at the local Medical College. The mansion remained in the Chazal family until 1966 when it was sold to the present owner who began an extensive restoration project. The original portico was removed and double wooden front doors with folding screens were added, as was the rounded brick terrace. The original transom was moved to become the front basement window, now visible at the lower left side of the building. It was also at this time that the local legendary blacksmith, Philip Simmons, was commissioned to design the new ironwork for the house. Mr. Simmons, born on June 9, 1912 on Daniel Island, is responsible for much of the ironwork added to Charleston structures and public buildings in the twentieth century. The pattern he developed for this home incorporates scrolls and hearts for the front gate, fencing, terrace portico, and lower level window grilles. The upstairs window grilles are a mixture of geometrical patterns including circles and rounded rectangles.

1. There are 7 panels in the fan design of the ornate ironwork near the entry. Square the number of panels and add 2.

2. If the square surrounding the circular design in the gate has a perimeter of 136 inches,

then determine 3 times the radius of the circle.

Meeting Street – Nathaniel Russell House Nathaniel Russell was a Northern expatriate who engaged in the import-export business. He was one of the wealthiest men at the time. Legend holds that this mansion was built to be a beautiful backdrop for his two available, but less than attractive, daughters. If true, this ploy was successful. This mansion faces the street, a departure from the single house style popular in Charleston. It is well known for its "flying" staircase and second story balconies. The exterior is a study in contrasts using two kinds of brick, wrought iron, wood, and marble. Today, the Historic Charleston Foundation operates this house as a museum.

1. Let x = the number of Russell’s daughters and y = this address. Evaluate: xy – 15

2. Suppose the outer radius of a brick arch over a 2nd story window is 2 feet. Using 22 7

for π, find the length of the outer semicircular arc for one window. Multiply this result by seven and add the street number for this address. From this result subtract 8·sin-1 π .

2

Church Street – Heyward Washington House The Heyward Washington House is located in the downtown Historic District, within the area of the original walled city. Daniel Heyward, a rice planter and founder of a prominent rice-planting dynasty, built the brick double house in 1772. He removed a two-story brick house from the site but may have kept the existing outbuildings. The house was the home of his son Thomas Heyward, a signer of the Declaration of Independence. President George Washington stayed here on his visit to the city in 1791. During the late 19th century, the lower left corner of the house was converted to a bakery. The house was restored in 1929 by the Charleston Museum and the Preservation Society of Charleston and is operated as a house museum by the Garden Club of Charleston.

1. Find the difference between the years George Washington stayed in this house on a visit and the building date. Now subtract one less than the number of stories in the house from that difference.

2. Let x = the radius of the semicircle above the door, given that the area of the

semicircle is 2π. Determine ½ the slope of the tangent line to the function y = 3x3 – 2x at x.

Chalmers Street – The Pink House Research indicates that John Breton constructed the “Pink House” between 1694 and 1712 as a tavern. It is constructed partly of Bermuda stone, a coral limestone imported in blocks from Bermuda as building material. The building's gambrel roof is one of a few surviving in Charleston. It may be the city's oldest building and may have been used in the world's oldest profession, since 18th Century Chalmers Street was at the center of Charleston's "red light" district. The building, once the studio of artist Alice R. Huger Smith, later became a law office.

1. The colorful stone and the colorful history of the Pink House places it in the "red light" district. If a traffic light is red for 60 seconds, green for 60 seconds, and yellow for 15 seconds, find the number of seconds in a complete cycle.

2. Let x = the total number of glass panes on the front of the house.

Evaluate: W(x) = x (x – 6) 17

Church Street – Dock Street Theatre The Dock Street Theatre is located in the shell of the old Planter’s Hotel, which was famous food as well as being the birthplace of Planter’s Punch. In 1838 an infamous guest of the hotel, Junius Brutus Booth allegedly attempted to murder his manager in one of the hotel’s rooms. The original Dock Street Theatre, which was the first building built specifically for theatrical performances in America, raised its curtain February 12, 1736 with a production of The Recruiting Officer. In 1935, the City of Charleston, as a Works Progress Administration project, remodeled the old Planter’s Hotel property as the new Dock Street Theatre. Dorothy and DuBose Heyward were in attendance when the Theatre reopened on November 26, 1936 with a repeat performance of The Recruiting Officer, photos of which ran in the newly established Life magazine. The plaster in the Theatre predates construction (1806) and was salvaged from the Ratcliffe-King House slated for demolition farther up the street.

1. Let x = the number of years between the first performance in the Theatre and the second performance of The Recruiting Officer in 1936. Evaluate: x – 64

2. Let n = the number of wrought iron archways on the front of the second floor balcony.

If y = -0.1(x – 2)2 + 27 is the equation for one of these archways, find n times the y- value of the vertex, then add one to this result.

Church Street – French Huguenot Church Today the church stands as the first and last French Protestant congregation in America. The present building is Charleston’s first example of Gothic Revival architecture and was completed at a cost of $12,000. On the exterior, ornamentation such as buttresses and lancet windows can be evidenced, while inside, the railed chancel can be seen beneath the original 1847 Henry Erben organ. The church was called the Church of the Tides due to the fact the Dock Street (now Queen Street) was originally a tidal creek.

1. Divide the original cost of the church building by 1000 and multiply that number by

itself or square it. Then add to that the ones digit of this street number.

2. For this problem, award 50 points for each true and 0 points for each false Visualize the curves above the lancet windows as a graph in the first quadrant on the interval [0, 10], and the vertex at P(5, 10). Determine whether the following are True(award 50 points) or False (award 0 points); then total the points. a. The curve is continuous at x = 5. b. The curve is differentiable at x = 5. c. The graph (on 0<x<5) of the derivative of the curve is above the x-axis. d. The graph (on 5<x<1 0) of the derivative of the curve is below the x-axis. e. The graph of the derivative is continuous at (5,0).


1. The circular stained glass window on the front of this church is filled with hearts. If the area of one of these hearts is 25 square inches, then find the area of all the hearts.

2. Consider one of the towers of this church as a cylinder with a cone on top. Using the

radius of each to be 3 feet and the height of the cylinder to be 14 feet and the height of the cone to be 7 feet, find the volume of the entire tower. Then subtract 262 from

the volume. (Use 22 for π.) 7




Answer Key

Trail #5 2, 16, 23-25-27, 45, 51, 87, 17, 135, 136, 150, 200 Trail #5 2 Meeting Street – Meeting Street Inn 16 Meeting Street – Calhoun Mansion 23, 25, 27 Meeting Street – Three Sisters’ House 45 Meeting Street – Philip Simmons Iron Work 51 Meeting Street – Nathaniel Russell House 87 Church Street – Heyward-Washington House 17 Chalmers Street – Pink House 135 Church Street – Dock Street Theater 136 Church Street – French Huguenot Church 150 Meeting Street – Circular Church 200 East Bay Street – Custom House


7 Meeting Street – Josiah Smith House This house has memories of a famous punch. The Charleston Club (1881-1927) made the famous punch “Charleston Club Punch” which called for “one volume green tea, one volume California brandy, one-fourth volume Santa Cruz rum, lemon juice and sugar to taste, ice, lemon peel and just before serving, one volume mineral water”. If Santa Cruz cannot be found, use Jamaica Rum, Bacardi rum will not do.

1. An antique pitcher representing 1 volume contains 56 ounces. How much Santa Cruz

rum is needed to make one recipe of Charleston Club Punch?

2. Suppose the semicircular portico has a diameter of 32 feet.

Evaluate in terms of π : 2(area of portico) − (arccos(−1)) ⋅ (60) π

Lamboll Street – The Wedding Cake House This house, with its elaborate exterior finish, was built c. 1850 by Patrick O'Donnell, a building contractor, who built his mansion around the corner at 21 King Street.

1. To this street number, add one-sixth the number of window panes in a window.

2. Suppose the semicircular attic vent on the right end of this house were divided into 10 circle sectors. Let x = the number of degrees in the central angle of a sector. Evaluate: x – 2

Meeting Street – Calhoun Mansion When construction was completed in 1876 at a cost of $200,000 an article in the News and Courier hailed the home as, “the handsomest and most complete private residence in the South.” Spanning some 24,000 square feet, the home is considered the largest single-family residence in the city. The style incorporates Italianate and Renaissance Revival styles. The structure features sweeping piazzas; walnut, oak and kingwood woodwork; fireplace and floor tiles by the Minton China Company; and a crystal ceiling in second floor music room. Augusta, Georgia merchant George Walton Williams built the home. His daughter later married the grandson of Vice- President John C. Calhoun.

1. Double the number of arches on the front of the house (including over entrances)

2. Let n = number of arches on the front of the house. Evaluate: lim x→0

2(x 2 − n2 ) x − n

Meeting Street - Thomas Heyward House The Thomas Heyward house was built around the year 1803. It is unclear whether Nathaniel Heyward or his brother Thomas Heyward, a signer of the Declaration of Independence, built this three-story home. There is a secret room on the second floor that was used to store wine. James T. Adger who operated the first coastal steamship line in the United States, lived in this home at one time.


1. Evaluate: current house # + number of stories in the house + floor of secret room

2. Determine 3 consecutive odd integers whose sum is 82 + (# of stories)2 + 2

, , Meeting Street – The Three Sisters’ Houses These houses are a group of Charleston single houses, built by a father to attract potential suitors for each of his three daughters. True to single house fashion, each house has one end that faces the street. All are three-story dwellings, have wrought iron balconies overlooking the street, and pretty gardens viewable through wrought iron gates. Albert Delmar is credited with building 23 Meeting Street around 1750. The molding above the top windows is often referred to as the “eyebrows” of this house. The first of the trio, 25 Meeting Street, was built while Charleston was still a colony. The second, 27 Meeting Street, has a basement that raises the first floor higher than the other two houses and has a hip roof. This last house was constructed after the Revolutionary War.

1. Begin with the number of sisters, subtract 1, then subtract that result from three times the sum of the digits of the year that 23 Meeting St. was built.

2. Let m = the number of sisters’ houses. Let x = 6(ln em)(logm mm). Reverse the digits

of x and subtract 8.

Meeting Street – Otis Mills House This house was built between the years of 1775 –1782. In 1809 William Brisbane, a planter, bought the home and later added the large bays on the front of the house. The next owner of this house was Otis Mills, who bought the house in 1848. In October 1862, Mr. Mills loaned the house to General Pierre G.T. Beauregard, who remained at the house until August 1863.

1. Divide the total number of degrees in one of the semicircular bays on the front of this house by nine and add this to the street number, then subtract 4.

2. General Beauregard used this house from Oct. 1862 through Aug. 1863. Assuming

occupancy from Oct. 1 to Aug. 31, let x = the number of months Confederate headquarters occupied the house and let y = the number of circular bays or turrets on the front of the house. Evaluate: 5x – y!

Meeting Street – First Scots Presbyterian Church In 1731, twelve Scottish families withdrew from the Independent or Congregational Church and founded the “Scots Kirk” or Scotch Meeting. The original frame building was replaced in 1814 by the present one. It is the fifth oldest church in the city and unique with its two towers. The seal of the Church of Scotland is in the window over the main entrance. The Church bell was given to the Confederacy in 1863 to be melted down for use as ammunition and was not replaced until May 1999.

1. To the street number of this church, add the number of Scottish families that founded it. Now add the number of this church in the order of oldest churches. Next, add to this the number of years the church was without a bell, multiply by ½, subtract 3 dozen, and lastly add 9.

2. Let x = the number of years the church was without a bell. If x = the nth term of the

sequence a1 = -14 and the common difference is 2, determine which term of the sequence is x.

Meeting Street – Judge Elihu Hall Bay House This home once belonged to a beloved Charleston judge who purchased the house in 1784. Less than two years later, he found himself sharing his home with a collection of spirits trapped there through a series of poor choices. Late on a dark August night in 1786, Judge Bay awoke to the sound of drunken men just outside his windows on St. Michael’s Alley. Suddenly, two foolish young men, who in their inebriated state decided to settle differences with a duel, fired shots. The judge threw open his windows in time to see six friends carrying a wounded body up his front stairs with the intention of leaving the dying man in the judge’s care. The unfortunate young man died in the upstairs front bedroom as a result of his injuries. Over the next century on calm nights, footsteps of six friends could be heard on the stairs carrying their dying friend to a soft bed. All were bound there, sentenced to relive that hot August night for an eternity. Relief came in 1942 when St. Michael’s Church purchased the house for use as its rectory. Since that time, the footsteps have ceased their hurried ascent upstairs.

1. Multiply the sum of the digits of the street number by the number of stories in the

house. Next add the street number to that product and then subtract ten.

2. Let n = the number of years that this house has served as a rectory. Evaluate: 2[n – 3(# of stories)] + 1

Meeting Street – Hibernian Hall Hibernian Hall was built in 1839 for $40,000 from the designs of a Philadelphia architect, Thomas U. Walter, who is best known for adding the great dome to the U.S. Capitol Building. The original portico collapsed in the earthquake of 1886 and was rebuilt in more elaborate form. The Irish harp is contained in the panel above the door as well as the overthrow of the iron gates. The ironwork design is attributed to Christopher Werner of Charleston. The Hibernian Society was formed in 1801 as an Irish Benevolent Society. Presidents of the society alternate between Catholic and Protestant, and membership is passed only from father to son. In early 1861, the state legislature temporarily moved to Charleston and met in Hibernian Hall. During this stay they adopted the state flag that has since been used in South Carolina. Of all the social functions held in Hibernian Hall, the St. Cecilia’s Society Ball is still the most famous.

1. Find the original cost of the Hibernian Hall per 1000 square feet. To this value, add

the number that is made from the digits in the tens place and ones place in the year that the Hibernian Hall was built. Subtract one from this result.

2. Let a = the sum of the digits in the year before the Hibernian Hall was built, b =

number of columns on the front of the building, c = the sum of the digits in the year that the state legislature temporarily moved to Charleston, and d = the number of

letters in the word Hibernian. Evaluate: a c

- 2(c – d)+d. b d

Cumberland – Powder Magazine A National Historic Landmark, the Powder Magazine is the oldest public building in South Carolina. Defense of the colony was a priority. To that end, fortified walls were constructed around the city. The Powder Magazine was built with brick walls 32 inches thick in 1713 to store the city's gunpowder. The interior roof structures were constructed so that the building would implode if an explosion were to occur inside. The steeply tiled roof, which was typical in that era, is gabled on all sides. The building has undergone an extensive archaeological and architectural conservation project, led by the Historic Charleston Foundation.

1. Convert the thickness of the brick walls in inches to feet. Truncate the fraction or decimal, then multiply by 10 decades.

2. If the “peak” of the roof directly above the entrance is represented by the equation y = - x + (age of building - 90), determine the absolute maximum of the “peak.”




Answer Key

Trail #6 7, 14, 16, 18, 23-25-27, 37, 53, 76, 105, 79, 200 Trail #6 7 Meeting Street – Josiah Smith House 14 Lamboll Street – The Wedding Cake House 16 Meeting Street – Calhoun Mansion 18 Meeting Street – Thomas Heyward House 23, 25, 27 Meeting Street – The Three Sisters’ Houses 37 Meeting Street – Otis Mills House 53 Meeting Street – First Scots Presbyterian Church 76 Meeting Street – Judge Elihu Hall Bay House 105 Meeting Street – Hibernian Hall 79 Cumberland – Powder Magazine 200 East Bay Street – Custom House


61 Church Street - First Baptist Church The First Baptist Church, the oldest Baptist church in the South, is called the "Mother Church” of Southern Baptists. Organized in Kittery, Maine this church was driven by persecution to South Carolina in 1683. In 1699, William Elliot donated the present lot on Church Street and a frame building was erected. The cornerstone of the present church was laid in September 1819. It was designed by architect Robert Mills, who considered it "the best specimen of correct taste in architecture of all the modern buildings in this city." Although Mills said the building was "purely Greek in its style," it actually has Tuscan columns and Roman arches.

1. Evaluate: (# full circles in windows) + (# of semicircular windows) + 4(# of rectangular windows) + 5(# of Tuscan columns)

2. Given ≈ 42.6497, round this decimal to the nearest whole number, add the sum of digits when cornerstone was laid, then subtract the expression

tan [arcsin (# rectangular windows) ] 10

# on cornerstone

Church Street - Ladd Brown House (also Thomas Rose House) Thomas Rose, an Ashley River planter, is said to have built this two and one-half story stuccoed brick house soon after his marriage to Beuler Elliot in 1733. The house has an asymmetrical plan typical of early Charleston houses, and early Georgian interiors with robust and simple paneling, staircase and other woodwork. The piazza is a 20th century addition. The house is said to be haunted by the ghost of Dr. Joseph Ladd Brown. In 1786 he was carried into the house after being mortally wounded in a duel, in which he defended the honor of an actress named Mrs. Robertson, nicknamed "Perdita."

1. Let (# people in the duel) - 1 = ones digit of next address and # letters in Mrs. Robertson's nickname = tens digit of next address.

2. A piazza is a large porch or veranda. If a = 1, b = 2 etc., evaluate: (sum of the values

of the letters in the word piazza) - (# of shutters on Church Street side of house) + 12

Church Street - Colonel Robert Brewton House The spirited woman who once owned this house, Mary Weyman Brewton Foster, talked back to a British officer, Lt. Col. Banastie Tarleton, and was banished to Philadelphia for her nimble wit and sharp tongue. The lieutenant colonel said, "I would like to see this fellow Washington of whom people talk so much." Whereupon Mrs. Foster retorted: "What a pity you did not look behind you at the Battle of Cowpens." The house, built in 1720, is one of Charleston's earliest examples of a single house.

1. Evaluate: 3(age in decades of house) – (# of trapezoids above front windows)

2. Given: h = 8 in., b1 = 13 in., b2 = 6 in. Find the area of one of the trapezoids above the windows and doors.

n

+ −

Church Street - DuBose Heyward House In this small, notable post-Revolutionary house, DuBose Heyward wrote Porgy, the novel on which the operetta Porgy and Bess was based. It was designated a National Historic Landmark in 1972. The house has been combined with 78 Church Street, another post-Revolutionary dwelling, into one residence. Tradition says President George Washington spoke from a balcony at 78 Church Street on his visit to Charleston in 1791. The present balcony, however, is in the Regency style of c. 1815-25. The third floor of 78 Church Street is partly supported by a mahogany bedpost.

1. Find the product of windows and shutters that face Church Street, take this result and add the number of earthquake bolts.

2. Refer to the title of the operetta written by Gershwin that was based on the novel

written by DuBose Heyward. Determine the probability that a letter chosen at random from this operetta title will be a vowel (not including y). Let this result represent the

number n. Evaluate: 5 2

1 n2

Church Street - Heyward Washington House The Heyward Washington House is located in the downtown Historic District, within the area of the original walled city. Daniel Heyward, a rice planter and founder of a prominent rice-planting dynasty, built the brick double house in 1772. He removed a two-story brick house from the site but may have kept the existing outbuildings. The house was the home of his son Thomas Heyward, a signer of the Declaration of Independence. President George Washington stayed here on his visit to the city in 1791. During the late 19th century, the lower left corner of the house was converted to a bakery. The house was restored in 1929 by the Charleston Museum and the Preservation Society of Charleston and is operated as a house museum by the Garden Club of Charleston.

1. Since this house once housed a bakery, evaluate (dozen)(days in a week) + (days in a school week)

2. Evaluate the sum of the sequence defined by ∑(7k + 5) , where n = the number of k =1

windows on the first floor façade on Church Street. Subtract one from this result.

n

Church Street – Cabbage Row Cabbage Row was named for the buildings along Church Street at Elliot Street where vegetable farmers would come to display their goods for sale. This valuable three-story double tenement of stuccoed brick was called "Cabbage Row" because black tenants there put cabbages for sale on the windowsills. This was partly the inspiration for "Catfish Row," the locale of DuBose Heyward's novel Porgy. A notable feature is the wrought iron grille in the entrance to the central arched passage.

1. If 8 cabbages were placed on each of the windowsills of this double tenement you will have a half dozen too many to equal the next address.

2. Let m = the number of windows on the Church Street façade. Find the y-coordinate

of the vertex of the parabola f(x) = x2 – 6x + m + 115

East Bay - Old Exchange The Old Exchange and Custom House was built in 1767-71. William Rigby Naylor was the architect of the building, which was constructed by the brothers Peter and John Adam Horlbeck. The building is reminiscent of exchanges in London, Liverpool, and Bristol. It originally had an open arcade on the first floor and an elegant assembly on the second. Twin stair towers that projected into East Bay Street were taken down in the early part of the 19th century. The building was conveyed to the Federal government in 1818 and became the Post Office. In 1912, the Rebecca Motte Chapter of the Daughters of the American Revolution began negotiating to acquire the property but did not occupy it until 1921. In 1972 restoration of the Exchange Building began at a cost $1,910,000. The restoration is a modern adaptation of the historic building and is not meant to be an exact replication of the original appearance. The stair towers for example, were replaced, not on the west front where they would again have impeded traffic, but on the east side.

1. Take the last two digits of the year that the Daughters of American Revolution began to negotiate for this property, then add 5.

2. Above the entrance to the Exchange building is a window consisting of three

concentric semicircles. Find the central angle in one of the sectors for the innermost semicircle and let this value be θ. Let n = the number of semicircular windows at the entrance. Evaluate the expression (tan θ)·(20 – n).

Chalmers Street - The Pink House Research indicates that John Breton constructed the “Pink House” between 1694 and 1712 as a tavern. It is constructed partly of Bermuda stone, a coral limestone imported in blocks from Bermuda as building material. The building's gambrel roof is one of a few surviving in Charleston. It may be the city's oldest building and may have been used in the world's oldest profession, since 18th Century Chalmers Street was at the center of Charleston's "red light" district. The building, once the studio of artist Alice R. Huger Smith, later became a law office.

1. If these Bermuda stones were rectangular solids, 2" X 2" X 58", determine ½ the volume of one stone.

2. Let n = # of earthquake bolts visible from the parking lot side of the house and let m

= the measure of one interior angle of a regular pentagon. Evaluate: m + n + 3

bell' s weight


1. Evaluate: (# bell tolls honoring firefighters of 9/11) ÷ 7 X 3 - (hour bell tolled daily to

tell time)

2. Evaluate: + 85

Church Street - Dock Street Theatre The Dock Street Theatre is located in the shell of the old Planter’s Hotel, which was famous food as well as being the birthplace of Planter’s Punch. In 1838 an infamous guest of the hotel, Junius Brutus Booth allegedly attempted to murder his manager in one of the hotel’s rooms. The original Dock Street Theatre, which was the first building built specifically for theatrical performances in America, raised its curtain February 12, 1736 with a production of The Recruiting Officer. In 1935, the City of Charleston, as a Works Progress Administration project, remodeled the old Planter’s Hotel property as the new Dock Street Theatre. Dorothy and DuBose Heyward were in attendance when the Theatre reopened on November 26, 1936 with a repeat performance of The Recruiting Officer, photos of which ran in the newly established Life magazine. The plaster in the Theatre predates construction (1806) and was salvaged from the Ratcliffe-King House slated for demolition farther up the street.

1. In the year that the Dock Street Theatre raised its curtain, let a = the thousands digit, b = the hundreds digit, and c = the tens digit. Evaluate: (c - a)(b + c)2

2. Refer to the values of a, b, and c found in question #1. Evaluate: a∑

+b+c

+ 2 i=a

ci




Answer Key

Trail #7 61, 59, 71, 76, 87, 89-91, 122, 17, 116, 135, 200 Trail #7 61 Church Street – First Baptist Church 59 Church Street – Ladd Brown House (also Thomas Rose House) 71 Church Street – Colonel Robert Brewton House 76 Church Street – DuBose Heyward House 87 Church Street – Heyward Washington House 89-91 Church Street – Cabbage Row 122 East Bay Street – Old Exchange 17 Chalmers Street – The Pink House 116 Meeting Street – Old Lower Fire Station 135 Church Street – Dock Street Theatre 200 East Bay Street – Custom House


59 Church Street - Ladd Brown House (also Thomas Rose House) Thomas Rose, an Ashley River planter, is said to have built this two and one-half story stuccoed brick house soon after his marriage to Beuler Elliot in 1733. The house has an asymmetrical plan typical of early Charleston houses, and early Georgian interiors with robust and simple paneling, staircase and other woodwork. The piazza is a 20th century addition. The house is said to be haunted by the ghost of Dr. Joseph Ladd Brown, who in 1786 was carried into the house after being mortally wounded in a duel, in which he defended the honor of an actress named "Mrs. Robertson," nicknamed "Perdita."

1. How many people were involved in the duel where Dr. Brown was killed? Subtract

one from that number and use it as the ones digit in the address of your next location. You will find the tens digit by the number of letters in Mrs. Robertson’s nickname.

2. A piazza is a large porch or veranda. Let a = 1, b = 2, c = 3, etc., add the digits for

each letter of the word “piazza”. To that sum, subtract the number of shutters on the first floor of the Church Street side of the house and increase the result by two.

Church Street – Colonel Robert Brewton House The spirited woman who once owned this house, Mary Weyman Brewton Foster, talked back to a British officer, Lt. Col. Banastie Tarleton, and was banished to Philadelphia for her nimble wit and sharp tongue. The lieutenant colonel said, "I would like to see this fellow Washington of whom people talk so much.” Whereupon Mrs. Foster retorted: "What a pity you did not look behind you at the Battle of Cowpens." The house is one of Charleston’s earliest examples of a single house.

1. This house was built in 1720, which makes it 283 years old today or approximately 28 decades old. Take that result and multiply it by three. Subtract the number of trapezoids above the front windows (not doors) and add the number of Church Street ground level front doors.

2. Above the windows and doors you will find a trapezoid. Find the area of one of these

using the formula: Area = 1 h(b + b ) , given the height is 8 inches, the top base is 13

2 1 2

inches and the bottom base is 6 inches.

Church Street – DuBose Heyward House In this small, notable post-Revolutionary house, DuBose Heyward wrote Porgy, the novel on which the operetta Porgy and Bess was based. It was designated a National Historic Landmark in 1972. The house has been combined with 78 Church Street, another post-Revolutionary dwelling, into one residence. Tradition says President George Washington spoke from a balcony at 78 Church Street on his visit to Charleston in 1791. The present balcony, however, is in the Regency style of c. 1815-25. The third floor of 78 Church Street is partly supported by a mahogany bedpost.

1. The diamond shapes in the gate at this house are geometrical shapes called rhombi

(singular-rhombus). How many sides does each of these rhombi have? Take this number and multiply it by the number formed by adding the digits in the year that this house was designated as National Historic Landmark. Finally add this product to the number of the floor that is supported by a mahogany bedpost.

2. Evaluate the determinant and then add 1: # of window panes in one window floor supported by bedpost

number of sides in a rhombus

number of sides in a pentagon

East Bay Street – Rainbow Row In the 1920s and 1930s, this line of valuable old houses was gradually changed from slums to a handsome residential neighborhood. Built as merchant's houses, some as early as 1740, the buildings originally had stores and counting houses on the first level, and residences above. The name "Rainbow Row," was coined in the 1930s when, for the first time in a generation, the buildings were painted in a variety of pastel shades.

1. Find the probability that a “W” would be drawn if all the letters in “Rainbow Row” were to be placed in bag. Multiply the result by 610.

2. The rainbow makes an interesting geometric shape called a parabola. Using this

equation for a parabola, determine the y-value of the vertex: y = −2(x − 45)2 + 122

East Bay Street – Old Exchange The Old Exchange and Custom House was built in 1767-71. William Rigby Naylor was the architect of the building, which was constructed by the brothers Peter and John Adam Horlbeck. The building is reminiscent of exchanges in London, Liverpool, and Bristol. It originally had an open arcade on the first floor and an elegant assembly on the second. Twin stair towers, which projected into East Bay Street, were taken down in the early part of the 19th century. The building was conveyed to the Federal government in 1818 and became the Post Office. In 1912, the Rebecca Motte Chapter of the Daughters of the American Revolution began negotiating to acquire the property but did not occupy it until 1921. In 1972 restoration of the Exchange Building began at a cost $1,910,000. The restoration is a modern adaptation of the historic building and is not meant to be an exact replication of the original appearance. The stair towers for example, were replaced, not on the west front where they would again have impeded traffic, but on the east side.

1. Take the last two digits of the year the Rebecca Motte Chapter of the Daughters of the

American Revolution began negotiating to acquire this property and add 5.

2. The twin stair towers that project onto East Bay Street are symmetrical. Take the number of letters in the word symmetrical and increase it by log2 64.

Chalmers Street – The Pink House Research indicates that John Breton constructed the “Pink House” between 1694 and 1712 as a tavern. It is constructed partly of Bermuda stone, a coral limestone imported in blocks from Bermuda as building material. The building's gambrel roof is one of a few surviving in Charleston. It may be the city's oldest building and may have been used in the world's oldest profession, since 18th Century Chalmers Street was at the center of Charleston's "red light" district. The building, once the studio of artist Alice R. Huger Smith, later became a law office.

1. If these imported Bermuda stones were rectangular solids with dimensions of 2 inches by 29 inches by 2 inches then find volume of one of them.

2. Take the number of earthquake bolts that are visible from the parking lot side of the

pink house and multiply it by the number of letters in the word that describes the shape of the geometric figure formed when imaginary lines are drawn to connect the bolts. Take this result and increase it by the last two digits of when the Declaration of Independence was signed.

Meeting Street – Old Lower Fire Station Built in 1887, the Flemish-bonded brick structure was completed at a cost of $7,000 as a strategic move to strengthen the City’s central fire warning system. The tower at the rear of the property contains a 2,500-pound iron bell. The bell was used for everything from alerting citizens to fire and hurricanes to notifying the public about important national events, and until 1927, as a means to tell time by tolling daily at 12:00 Noon. The Old Lower Fire Station has been converted to city offices; however, it remained active as a fire station, keeping watch over its citizens, until 1953. Today, the bell is silent except when used ceremonially. It most recently rang 343 times, once for each firefighter lost in the September 11th World Trade Center tragedy.

1. Take the number of times the bell rang for the firefighters lost on Sept. 11th and subtract 193.

2. Take the square root of the weight of the bell, and increase the result by the square of

10.


1. The circular window has hearts in it. Divide the number of degrees in a circle by the number of hearts and multiply that by two. Decrease your result by the number of windows in the bell tower, and then add 1.

2. Evaluate: ln e229 - (number of windows in bell tower)2 - 6

12

Cumberland – Powder Magazine A National Historic Landmark, the Powder Magazine is the oldest public building in South Carolina. Defense of the colony was a priority. To that end, fortified walls were constructed around the city. The Powder Magazine was built with brick walls 32 inches thick in 1713 to store the city's gunpowder. The interior roof structures were constructed so that the building would implode if an explosion were to occur inside. The steeply tiled roof, which was typical in that era, is gabled on all sides. The building has undergone an extensive archaeological and architectural conservation project, led by the Historic Charleston Foundation.

1. Find the number of feet in the wall’s thickness multiply this by three fourths of 100.

2. Given the arithmetic sequence such that: a0 = current address, d = 10. Find a and then add 1. (a12 is the 13th term)




Answer Key

Trail #8 59, 71, 76, 79-107, 122, 17, 116, 150, 79, 200 Trail #8 59 Church Street – Ladd Brown House (also Thomas Rose House) 71 Church Street – Colonel Robert Brewton 76 Church Street – DuBose Heyward House 79-107 East Bay Street – Rainbow Row 122 East Bay Street – Old Exchange 17 Chalmers Street – The Pink House 116 Meeting Street – Old Lower Fire Station 150 Meeting Street – Circular Church 79 Cumberland – Powder Magazine 200 East Bay Street – Custom House


21 East Battery - Edmonston-Alston House Charles Edmonston was a Scotsman who made his fortune as a merchant. He had this house built circa 1829 on the site of one of Charleston's first defenses, Fort Mechanic. This fort was built in 1795 by the mechanics of Charleston. Carpenters and other artisans worked free of charge to protect the young nation. The house was sold in 1839 to satisfy debts totaling $125,000 to Charles Alston. This distinguished family included Theodosia Burr Alston, Aaron Burr's daughter, who was the wife of South Carolina's governor. Sadly, she was lost at sea. Today, the Historic Charleston Foundation operates the main house as a museum.

1. Let n = the number of floors of the house, evaluate: (n 2 − 1) (2n – 1) + n.

2. Let n = the number of windows on the first floor facing East Battery. Evaluate the complex number: 40 – 3in.

windows

East Bay - Home of the bride of “Mad Archie Campbell” This house (c. 1755) stands on part of Lot No. 1 of the Grand Modell, which was granted to Maurice Matthews and James Moore by the Lord Proprietors in 1682. It was owned by George Sommers and remained in the Sommers’ family until the 1790s. The bend in East Bay where it connects to East Battery was also known as “Sommer’s Corner”. Another interesting story about this house is that one of its inhabitants has a ghost tale. Miss Paulina (Polly) Phelps was the girlfriend of Captain Archie Campbell (Mad Archie Campbell). Archie had made a wager that he would marry Polly with her consent in three days or lose his Arabian Philly. He arrived at her home to take her on an afternoon ride in the country. When they arrived at the Goose Creek Church and told the minister at gunpoint to marry them or be shot. The minister asked if the lady consented and Archie pointed the gun at his Paulina as he said “the lady does consent” and she said “yes.” They were very happy together living on Exeter Plantation, but for only a short time for Archie was killed and Paulina died shortly afterwards. The ghost tale says that Paulina returns to Exeter in search of their baby she left behind.

1. Let n = the year that Lot No. 1 was granted to Maurice Matthews and James Moore by the Lord Proprietors. Evaluate: n - 40 2 - 3 x 7

2. Let [ A] be a 2x2 matrix with the following entries that refer to the East Battery facade of the house. Find the determinant of the matrix.

# panes in one1st floor window 7

# floors in house + 2 # shutters on1st floor windows

Church Street - First Baptist Church The First Baptist Church, the oldest Baptist church in the South, is called the "Mother Church” of Southern Baptists. Organized in Kittery, Maine, this church was driven by persecution to South Carolina in 1683. In 1699, William Elliot donated the present lot on Church Street and a frame building was erected. The cornerstone of the present church was laid in September 1819. It was designed by architect Robert Mills, who considered it "the best specimen of correct taste in architecture of all the modern buildings in this city." Although Mills said the building was "purely Greek in its style," it actually has Tuscan columns and Roman arches. Mills may also have designed the iron gates and fence, which are of Guilloche design of alternating curves and lozenges.

1. Let n = the sum of the degrees of the semicircular windows above the doors facing

the street. Evaluate: n

+ 5 10

2. Approximate the circumference of the arch above one of the semicircular windows at

the entrance to the church, using 22 for π and assume the diameter of the arch is 7 7

feet. Evaluate: 6(circumference of this semicircle - 1) + cos(# of degrees in a semicircle)

Church Street – Ladd Brown House (also Thomas Rose House) Thomas Rose, an Ashley River planter, is said to have built this two and one-half story stuccoed brick house soon after his marriage to Beuler Elliot in 1733. The house has an asymmetrical plan typical of early Charleston houses, and early Georgian interiors with robust and simple paneling, staircase and other woodwork. The piazza is a 20th century addition. The house is said to be haunted by the ghost of Dr. Joseph Ladd Brown, who in 1786 was carried into the house after being mortally wounded in a duel, in which he defended the honor of an actress named "Mrs. Robertson," nicknamed "Perdita."

1. Begin with the year Dr. Brown was mortally wounded at this house, subtract the house

number, subtract 1700, multiply by 3, and then subtract 10.

2. A “piazza” is a large porch or veranda. Find the number of arrangements of the letters in the word “piazza”. Take this result, divide it by three, and then add eleven.

Church Street - Colonel Robert Brewton House The spirited woman who once owned this house, Mary Weyman Brewton Foster, talked back to a British officer, Lt. Col. Banastie Tarleton, and was banished to Philadelphia for her nimble wit and sharp tongue. The lieutenant colonel said, "I would like to see this fellow Washington of whom people talk so much." Whereupon Mrs. Foster retorted: "What a pity you did not look behind you at the Battle of Cowpens." The house is one of Charleston's earliest examples of a single house.

1. Let n = the number of windows facing the street. Evaluate: 900% of n + 50% of n.

2. The wrought iron balcony of the house encloses a small area that looks like the drawing below. Assume the following measurements: radius of the semicircle = 2 feet, length of the rectangular region = 8 feet, and width of the rectangular region = 3 feet. Evaluate: 3[cos(area of semicircle) + area of rectangular region] + 1

Church Street - DuBose Heyward House In this small, notable post-Revolutionary house, DuBose Heyward wrote Porgy, the novel on which the operetta Porgy and Bess was based. It was designated a National Historic Landmark in 1972. The house has been combined with 78 Church Street, another post-Revolutionary dwelling, into one residence. Tradition says President George Washington spoke from a balcony at 78 Church Street on his visit to Charleston in 1791. The present balcony, however, is in the Regency style of c. 1815-25. The third floor of 78 Church Street is partly supported by a mahogany bedpost.

1. DuBose Heyward wrote the novel Porgy at this house. Assigning each letter of the alphabet to a number, beginning with A = 1, B = 2, etc., determine the sum of the letters in the title Porgy and then add six.

2. Refer to the title of the operetta written by Gershwin that was based on the novel

written by DuBose Heyward. Determine the probability that a letter chosen at random from this operetta title will be a vowel (not including y). Let this result represent the number n. Evaluate the expression 5

+ 2 −1 .

n2 n

Church Street - Heyward Washington House Daniel Heyward, a rice planter and founder of a prominent rice-planting dynasty, built this brick double house in 1772. He removed a two-story brick house from the site but may have kept the existing outbuildings. The house was the home of his son Thomas Heyward, a signer of the Declaration of Independence. President George Washington stayed here on his visit to the city in 1791. During the late 19th century, the lower left corner of the house was converted to a bakery. The house was restored in 1929 by the Charleston Museum and the Preservation Society of Charleston and is operated as a house museum by the Garden Club of Charleston.

1. Let n = the number of red brick steps at doorway. Evaluate: n 3 + n 2 + n – 5.

2. Evaluate the sum of the sequence defined by ∑(8k −1) , where n = the number of k =1

windows on the first floor façade on Church St. Add three to this sum.

n

East Bay - Rainbow Row "Rainbow Row" is a name coined in the 1930s because these homes were painted in a variety of pastel colors. From a slum to a highly sought after neighborhood, these houses were gradually changed, beginning in the 1920s and '30s. Built as merchant's houses, some as early as 1740, the buildings originally had stores and counting houses on the first level and residences above.

1. Let n = the first year of the decade in which the name was coined and let m = the year

the earliest house was built. Evaluate: 2(n − m) −14

3

2. A rainbow is sometimes called the “circle of light”. Find the y-coordinate of the center of the circle whose equation is (x − 3)2 + ( y −122)2 = 36 .

East Bay - Old Exchange The Old Exchange and Custom House was built in 1767-71. William Rigby Naylor was the architect of the building that was constructed by the brothers Peter and John Adam Horlbeck. The building is reminiscent of exchanges in London, Liverpool, and Bristol. It originally had an open arcade on the first floor and an elegant assembly on the second. Twin stair towers, which projected into East Bay Street, were taken down in the early part of the 19th century. The building was conveyed to the Federal government in 1818 and became the Post Office. In 1912, the Rebecca Motte Chapter of the Daughters of the American Revolution began negotiating to acquire the property but did not occupy it until 1921. In 1972 restoration of the Exchange Building began at a cost $1,910,000. The restoration is a modern adaptation of the historic building and is not meant to be an exact replication of the original appearance. The stair towers for example, were replaced, not on the west front where they would again have impeded traffic, but on the east side.

1. Let N = the sum of the degrees of the 3 rectangular windows. Let M = the sum of the angle measures of the 3 semicircular windows. What percent of M is N?


concentric semicircles. Find the central angle in one of the sectors for the innermost semicircle and let this value be your value forθ . Evaluate the expression: 2 tanθ ⋅102 .

East Bay Street at Market Street - Custom House With funds appropriated by Congress in 1848, the site of Fitzsimons’ Wharf was bought in 1849 to build the US Custom House. During excavation of the basement, the remains of Craven’s Bastion, a colonial-era fortification, were found. The building’s construction, interrupted by the Civil War, was completed in 1879 as it is today. Marble was used for the two upper floors. Roman Corinthian porticos, engaged columns, and entablature (the section that lies between the columns and the roof) surround the cruciform (shaped like a cross) building. Emile T. Viett carved the marble capitals and decorative work.



Answer Key

Trail #9 21, 43, 61, 59, 71, 76, 87, 79-107, 122, 200 Trail #9 21 East Battery – Edmonston-Alston House 43 East Bay – Home of the Bride of “Mad Archie Campbell” 61 Church Street – First Baptist Church 59 Church Street – Ladd Brown House (also Thomas Rose House) 71 Church Street – Colonel Robert Brewton House 76 Church Street – DuBose Heyward House 87 Church Street – Heyward Washington House 79-107 East Bay – Rainbow Row 122 East Bay – Old Exchange 200 East Bay Street – Custom House


43 East Bay - Home of the bride of “Mad Archie Campbell” This house (c. 1755) stands on part of Lot No. 1 of the Grand Modell, which was granted to Maurice Matthews and James Moore by the Lord Proprietors in 1682. It was owned by George Sommers and remained in the Sommers’ family until the 1790s. The bend in East Bay where it connects to East Battery was also known as “Sommer’s Corner”. Another interesting story about this house is that one of its inhabitants has a ghost tale. Miss Paulina (Polly) Phelps was the girlfriend of Captain Archie Campbell (Mad Archie Campbell). Archie had made a wager that he would marry Polly with her consent in three days or lose his Arabian Philly. He arrived at her home to take her on an afternoon ride in the country. When they arrived at the Goose Creek Church and told the minister at gunpoint to marry them or be shot. The minister asked if the lady consented and Archie pointed the gun at his Paulina as he said “the lady does consent” and she said “yes.” They were very happy together living on Exeter Plantation, but for only a short time for Archie was killed and Paulina died shortly afterwards. The ghost tale says that Paulina returns to Exeter in search of their baby she left behind.

1. Let n = year that this lot #1 was granted to Maurice Matthews and James Moore by the

Lord Proprietors. Evaluate: n

− 11 2

2. Let n = the sum of the digits in the year the lot was granted to Matthews and Moore by n − 1

9 4

n −1 the Lord Proprietors. Evaluate:

+10 sin 4 − 2 4

Meeting Street - Thomas Heyward House The Thomas Heyward house was built around the year 1803. It is unclear whether Nathaniel Heyward or his brother Thomas Heyward, a signer of the Declaration of Independence, built this three-story home. There is a secret room on the second floor that was used to store wine. James Adger lived in this home at one time. He operated the first coastal steamship line in the United States.


1. Let a = the number of stories of the house. Evaluate: a2 (2a – 1)

2. Let n= the number of the floor of the house where a secret wine closet is located and m

m= the number of floors in the house. Evaluate ∫3xn dx 0

+ m2(n)

Meeting Street - Phillip Simmons Iron Work A local French Huguenot family, the Chazals, built this Victorian gem in 1889. Dr. Chazal was a participating doctor at the local Medical College. The mansion remained in the Chazal family until 1966 when it was sold to the present owner who began an extensive restoration project. The original portico was removed and double wooden front doors with folding screens were added, as was the rounded brick terrace. The original transom was moved to become the front basement window, now visible at the lower left side of the building. It was also at this time that the local legendary blacksmith, Philip Simmons, was commissioned to design the new ironwork for the house. Mr. Simmons, born on June 9, 1912 on Daniel Island, is responsible for much of the ironwork added to Charleston structures and public buildings in the twentieth century. The pattern he developed for this home incorporates scrolls and hearts for the front gate, fencing, terrace portico, and lower level window grilles. The upstairs window grilles are a mixture of geometrical patterns including circles and rounded rectangles.

1. Use this gate to find a 2-digit number. To find the tens digit add the number of hearts

and one-half the number of teardrops on the gate. The number of brass flowers on the gate gives the ones digit.

2. Let x = the number of teardrop designs in the circle on the gate. Find the sixth term of

the arithmetic sequence for which a0 = 41 and the common difference is x.

Church Street - First Baptist Church The First Baptist Church, the oldest Baptist church in the South, is called the "Mother Church” of Southern Baptists. Organized in Kittery, Maine, this church was driven by persecution to South Carolina in 1683. In 1699, William Elliot donated the present lot on Church Street and a frame building was erected. The cornerstone of the present church was laid in September 1819. It was designed by architect Robert Mills, who considered it "the best specimen of correct taste in architecture of all the modern buildings in this city." Although Mills said the building was "purely Greek in its style," it actually has Tuscan columns and Roman arches. Mills may also have designed the iron gates and fence that are of Guilloche design of alternating curves and lozenges.

1. Let n = sum of the degrees in the semicircular windows above the doors facing the

street. Evaluate: n + 5

10

2. Approximate the circumference of the arch above one of the semicircular windows at

the entrance to the church, using 22 for π. Assume the diameter of the arch is 7 feet 7

and calculate the circumference. Evaluate: 6(circumference of this semicircle - 1) + cos(# of degrees in a semicircle)

Church Street – Ladd Brown House (also Thomas Rose House) Thomas Rose, an Ashley River planter, is said to have built this two and one-half story stuccoed brick house soon after his marriage to Beuler Elliot in 1733. The house has an asymmetrical plan typical of early Charleston houses, and early Georgian interiors with robust and simple paneling, staircase and other woodwork. The piazza is a 20th century addition. The house is said to be haunted by the ghost of Dr. Joseph Ladd Brown, who in 1786 was carried into the house after being mortally wounded in a duel, in which he defended the honor of an actress named "Mrs. Robertson," nicknamed "Perdita."

1. Begin with the year that Dr. Brown was mortally wounded at this house, subtract the

house number, subtract 1700, multiply by 3 and subtract 10.

2. A “piazza” is a large porch or veranda. Find the number of arrangements of the letters in the word “piazza”. Take this result, divide it by three, and then add eleven.

n

Church Street - Colonel Robert Brewton House The spirited woman who once owned this house, Mary Weyman Brewton Foster, talked back to a British officer, Lt. Col. Banastie Tarleton, and was banished to Philadelphia for her nimble wit and sharp tongue. The lieutenant colonel said, "I would like to see this fellow Washington of whom people talk so much." Whereupon Mrs. Foster retorted: "What a pity you did not look behind you at the Battle of Cowpens." The house is one of Charleston's earliest examples of a single house.

1. Let n = the number of windows facing the street. Evaluate 900% of n + 50% of n.

2. Let n= the number of trapezoids on the facade of the building on Church Street.

Evaluate: (arctan 4 n ) + ( +1)2 . (Express your angle in degrees.)

Church Street – DuBose Heyward House In this small, notable post-Revolutionary house, DuBose Heyward wrote “Porgy,” the novel on which the operetta “Porgy and Bess” was based. It was designated a National Historic Landmark in 1972. The house has been combined with 78 Church Street, another post-Revolutionary dwelling, into one residence. Tradition says President George Washington spoke from a balcony at 78 Church Street on his visit to Charleston in 1791. The present balcony, however, is in the Regency style of c. 1815-25. The third floor of 78 Church Street is partly supported by a mahogany bedpost.

1. Let n = the difference between the year in which this house was designated a National

Historic Landmark and the year George Washington visited Charleston. Determine 2 consecutive odd numbers whose sum is n - 1.

2. Refer to the operetta written by Gershwin, which was based on the novel by DuBose

Heyward. Let n = the probability that a letter chosen at random from this title will be a vowel (a,e,i,o,u). Evaluate: n-3 + (n-1 + 1)2

Church Street - Cabbage Row Cabbage Row was named for the buildings along Church Street at Elliot Street where vegetable farmers would come to display their goods for sale. This valuable three story double tenement of stuccoed brick was called "Cabbage Row" because black tenants there put cabbages for sale on the windowsills. This was partly the inspiration for "Catfish Row," the locale of DuBose Heyward's novel Porgy. A notable feature is the wrought iron grille in the entrance to the central arched passage.

1. Assign each letter of the alphabet to a number, beginning with A = 1, B = 2, etc.

Determine the sum of the letters in Cabbage Row. Evaluate: sum + 45.

2. Let n = the number of letters in Cabbage Row. Evaluate log n122

East Bay - Old Exchange The Old Exchange Building was built in 1767-71. This building is similar to the exchanges in London, Liverpool, and Bristol. The formal entrance was on the waterside where arriving royal governors, as well as President George Washington who visited in 1791, were greeted. A magnificent concert and ball were held in this building along with the many entertainments given for Washington in the week he was here. Ladies of the city wore "fillets" or bandeaux in their hair, with pictures of Washington and the words "Long Live the President" in gilt letters. The Old Exchange Commission was established in 1976 for the purpose of leasing and renovating the building. The restoration, paid for with state and federal funds, cost $1,910,000 and was completed in 1979-83. The Old Exchange and Provost Dungeon, however, was reopened in 1981, as a museum and meeting place. The restoration is a modern adaptation of the historic building and is not meant to be an exact replication of the original appearance. The stair towers for example, were replaced, not on the west front where they would again have impeded traffic, but on the east side. Portions open to the public include the reconstructed Great Hall and the Provost Dungeon from which can be seen an excavated portion of the Half Moon Battery.

1. Let N = the sum of the angle measures of the 3 rectangular windows. Let M = the sum of the degrees in the 3 semicircular windows. Determine what percent of M is N.


concentric semicircles. Find the central angle in one of the sectors for the innermost semicircle and let this value be your value forθ . Evaluate the expression: 2 tanθ ⋅102 .

East Bay Street at Market Street – Custom House With funds appropriated by Congress in 1848, the site of Fitzsimons’ Wharf was bought in 1849 to build the US Custom House. During excavation of the basement, the remains of Craven’s Bastion, a colonial-era fortification, were found. The building’s construction, interrupted by the Civil War, was completed in 1879 as it is today. Marble was used for the two upper floors. Roman Corinthian porticos, engaged columns, and entablature (the section that lies between the columns and the roof) surround the cruciform (shaped like a cross) building. Emile T. Viett carved the marble capitals and decorative work.



Answer Key Trail #10 43, 18, 45, 61, 59, 71, 76, 89-91, 122, 200 Trail #10 43 East Bay – Home of the bride of Mad Archie Campbell 18 Meeting Street – Thomas Heyward House 45 Meeting Street – Philip Simmons Iron Work 61 Church Street – First Baptist Church 59 Church Street – Ladd Brown House (also Thomas Rose House) 71 Church Street – Colonel Robert Brewton House 76 Church Street – DuBose Heyward House 89-91 Church Street – Cabbage Row 122 East Bay Street – Old Exchange 200 East Bay Street – Custom House

Charleston Math Trails Map Locations

1 HANDKERCHIEF HOUSE 131 TRADD 2 CATHEDRAL OF ST. JOHN 120 BROAD 3 STUART HOUSE 106 TRADD 4 SWORD GATE HOUSE 32 LEGARE 5 LIBRARY GHOST 31 LEGARE 6 SIMMONS-EDWARDS HOUSE 14 LEGARE 7 21 KING 21 KING 8 2 LADSON 2 LADSON 9 MARKET HALL 184 MEETING 10 POWDER MAGAZINE 79 CUMBERLAND 11 CIRCULAR CHURCH 150 MEETING 12 MILLS HOUSE HOTEL 115 MEETING 13 OLD FIREHOUSE 116 MEETING 14 HIBERBIAN HALL 105 MEETING 15 ST. MICHAEL’S CHURCH 80 MEETING 16 JUDGE BAY HOUSE 76 MEETING 17 HORRY HOUSE 59 MEETING 18 FIRST SCOTS 53 MEETING

PRESBYTERIAN 19 PHILIP SIMONS IRON 45 MEETING 20 OTIS MILLS HOUSE 37 MEETING 21 THREE SISTERS 23, 25, 27 MEETING 22 THOMAS HEYWARD HSE 18 MEETING 23 WEDDING CAKE HSE 14 LAMBOLL 24 CALHOUN MANSION 16 MEETING 25 7 MEETING 7 MEETING 26 2 MEETING ST INN 2 MEETING 27 ST. PHILIP’S CHURCH 146 CHURCH 28 DOCK STREET THEATRE 135 CHURCH 29 FRENCH HUGUENOT CHR 136 CHURCH 30 PINK HOUSE 17 CHALMERS 31 CABBAGE ROW 89-91 CHURCH 32 HEYWARD-WASHINGTON HSE 87 CHURCH 33 DUBOSE HEYWARD HSE 76 CHURCH 34 71 CHURCH 71 CHURCH 35 LADD HOUSE 59 CHURCH 36 FIRST BAPTIST CHURCH 61 CHURCH 37 OLD EXCHANGE & DUNGEON 122 EAST BAY 38 RAINBOW ROW 79-107 EAST BAY 39 CAMPBELL HOUSE 43 EAST BATTERY 40 EDMONSTON-ALSTON HSE 21 EAST BATTERY 41 CUSTOM HOUSE 200 EAST BAY 42 NATHANIEL RUSSELL HOUSE 51 MEETING 43 JONATHAN BADGER HOUSE 12 ORANGE

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Documents

2003 Math Trails Committee Group Experience · Legare Street - Library Ghost House Mrs. William Heyward, a successful rice planter and sister-in-law of Thomas Heyward, signer of the