Your Location on Planet Earth The intersection of two lines
(longitude and latitude) specify a unique place on earth (G)
Coordinate systems; Spherical Geometry;(F)Functions
Slide 3
Your Location on Planet Earth The are other ways and systems to
determine your location on earth which we will not use; such as GPS
(Global Positioning System) coordinates have become popular as they
give real-time coordinates and a location based on satellites
orbiting earth UTM (Universal Transverse Mercator) is a system that
divides the earth into 60 zones that are 6 degrees wide and uses
the metric system (G)Coordinate systems
Slide 4
Longitude Definition : a measurement of distance, given in
degrees east or west of the prime meridian. The prime meridian is a
line that runs through the Greenwich Observatory in London,
England. On a map or globe, lines of longitude are drawn from the
North Pole to the South Pole (NASA, 2015). (MD) Measurement and
Data
Slide 5
Latitude Definition: a measurement of distance, given in
degrees north or south from the equator. Latitude lines are also
called Parallels (NASA, 2015).equator (MD) Measurement and Data (G)
Parallel Planes
Slide 6
Planning a Trip Rationale and Context Ive frequently taken
trips on foot, but have a limited sense of direction Id like to get
a better sense of direction using a compass and see the accuracy of
this method of navigation The following trip Ive made often and
wished to analyze it using a map and compass From: Downtown
Burlington, Cherry Street To: Saint Michaels College Traveling by
foot and bicycle Map: free from USGS (United States Geological
Survey)
Slide 7
Understanding a Map A topographic map represents a three
dimensional view of a specific part of the earth The USGS provides
free topographic maps of most parts of the United States
Topographic maps are printed in color with green showing
vegetation, white showing open terrain, and black used for man-made
features such as trails, roads, and bridges Contour lines or
elevation lines (brown lines) show where hills, mountains, valleys,
and canyons are located (G) (MD) Topographical analysis (2D-3D
geometry)
Slide 8
USGS Maps The United States is divided into quadrants based on
lines of latitude and longitude Each quadrant is often named after
significant geographical features or the city or town falling
within the quadrants boundaries (G)Coordinate systems
Slide 9
Dividing Degrees into Smaller Angle Measurements Each degree
can be divided into 60 minutes. (1 degree = 60) Similarly, 1 minute
can be divided into 60 seconds. (1 = 60) (G) Angles; (RP) Ratios
and Proportional Relationships; (NF) Number and
OperationsFractions
Slide 10
A Maps Area of Coverage USGS prints maps in what is known as
series 7.5 Minute series (most common), and 15 Minute series These
maps also feature other ways of determining your position on the
map or globe which we will not focus on such as the UTM system.
(RP) Scales(G)Coordinate systems
Slide 11
What is the area of coverage of a 7.5 series map? Convert 7.5
minutes (7.5) into degrees? So, a 7.5 minute series map shows an
area of the earths surface that is 7.5 minutes of longitude wide by
7.5 minutes of latitude high (RP) Scales; (MD) Measurement and
Data; (NF) Number and OperationsFractions
Slide 12
A Maps Scale In a 7.5 minute map the scale will be 1:24,000.
So, one unit of measurement on the map will be equal to 24,000
units of the same measurement actual size. In a 1:24,000 scale map
one inch equals about four-tenths of a mile or about 2,000 ft. The
scale on a map is also given in kilometers and meters. The scale
also shows what contour intervals represent. For this map between
contour intervals there is an increase or decrease of elevation of
about 20 Feet. (RP) Scales; Measurement and Data (MD)
Slide 13
Finding Longitude and Latitude on a Map Degrees of longitude
and latitude are indicated in the corners of the map. Looking a the
bottom left corner we see the following So the bottom left corner
tells us that longitude starts at 73 degrees 15 minutes, while the
latitude starts at 44 degrees 22 minutes and 30 seconds. (RP)
Scales; Measurement and Data (MD)
Slide 14
Latitude Looking at our map we have the following: Latitude
starts at 44 degrees 22 30. The next mark indicates 25. Since
latitude increases as one goes north The next tick mark is 230 from
the initial mark (2230 + 230 = 25 0) A similar analysis can be done
for longitude (RP) Scales; Measurement and Data (MD)
Slide 15
Finding the Maps area of interest (G) (MD) Topographical
analysis (2D-3D geometry)
Slide 16
The Compass (G) Angles A compass is a magnet. Since the earth
has magnetic properties it acts like a large magnet. A compass
points toward the earths magnet north. Maps are oriented to show
geographic north.
Slide 17
Declination Since maps show geographic north, while a compass
points to the earths magnetic north an adjustment needs to be made
in the field. Fortunately, maps indicate the angular difference
between the two which varies depending on your location on earth.
Declination is either west or east depending on which side of
geographic north the compass needle points. Declination is west
approximately 15 degrees for this trip (see above) So the compass
will have to be adjusted about 15 degrees WEST to compensate (G)
Angles
Slide 18
Compass Basics (G) Angles
Slide 19
Compass Basics A compass usually features A arrow indicating
that direction of travel A needle which acts as a magnet with clear
north and south polarity within a sealed fluid A rotating housing
ring with 360 degrees, the cardinal directions N, S, E, and W. A
orienting arrow which allows the needle to be boxed A built in
declination adjustment that allows the orienting arrow to be
adjusted to read true geographic north Useful scales of measurement
on the baseplate (G) Angles
Slide 20
Planning the Trip In designing this trip I used GeoGebra
dynamic geometry software after uploading an image to determine the
angles at each turn. (G) Angles; Lines of Intersection; Parallel
Lines
Slide 21
Planning the Trip in Stages Measurement and Data (MD) (G)
Angles; Lines of Intersection Total trip distance: approximately
2.8 miles
Slide 22
Taxicab Geometry (G) Angles; (MD) Measurement and Data;
(F)Functions: Distance
Slide 23
Using a Map and Compass A map gives you the lay of the land in
miniature To use a map effectively you must orient the geographical
map image to the land To do this is fairly simple if you can
identify landmarks and spin the map to match those landmarks (G)
Angles
Slide 24
Using a Map and Compass First, the compass must be adjusted for
declination Next, line up your compass with the longitude of the
map or a line parallel to it. Then, with the compass on a line
parallel to the north south longitude line on your map and in a
location with a landmark you can sight north you rotate the map and
compass together until the compass needle is boxed within the
orienting arrow Sight your next landmark, adjust the compass
housing to the direction of travel, rotate the map and compass
together until the compass needle is boxed within the orienting
arrow Follow the direction of travel with the compass until you
reach your landmark and sight a new one that requires you to change
direction or stay the course Repeat this process as you sight each
landmark on your trip (G) Angles; Coordinate systems: translations
of parallel lines
Slide 25
The Trip in Video (G) (MD) Topographical analysis (2D-3D
geometry)
Slide 26
Works Cited Hodgson, M. (1997). Compass and Map Navigator: The
complete guide to staying found. Riverton, WY: The Brunton Company.
How Stuff Works. (2006). How Compasses Work: Pole Magnetism
[Photograph], Retrieved April 20, 2015, from:
http://adventure.howstuffworks.com/outdoor-activities/hiking/compass1.htm
International GeoGebra Institute. (2015). GeoGebra (Version 5.0)
[Software]. Available from: http://www.geogebra.org/ Knot Working
(n.d.). Latitude-Longitude Grid [Photograph], Retrieved April 20,
2015, from:
http://knot-workin.com/images/client/Latitude-longitude-grid.gif
NASA. (2014, October 9). Latitude. Retrieved from
http://www.nasa.gov/audience/forstudents/k-4/dictionary/Latitude.html#.VRvzZOEYF2A
NASA. (2014). Latitude [Photograph], Retrieved April 20, 2015,
from:
http://www.nasa.gov/audience/forstudents/k-4/dictionary/Latitude.html#.VRvzZOEYF2A
NASA. (2014, October 9). Longitude. Retrieved from
http://www.nasa.gov/audience/forstudents/k-4/dictionary/Longitude.html#.VRvzC-EYF2B
NASA. (2014). Longitude [Photograph], Retrieved April 20, 2015,
from:
http://www.nasa.gov/audience/forstudents/k-4/dictionary/Longitude.html#.VRvzC-EYF2B
NASA. (2014). Prime Meridian [Photograph], Retrieved April 20,
2015, from: http://www.nasa.gov/audience/forstudents/k-
4/dictionary/Prime_Meridian.html#.VRvzQeEYF2A Pingstone, A. (2009).
Walkers Compass [Photograph]. Retrieved April 20, 2015, from:
http://commons.wikimedia.org/wiki/File:Walkers_compass_arp.jpg USGS
Store: Map Locator and Downloader. (2012).
VT_Burlington_20120607_TM_geo.pdf [Data file]. Retrieved from
http://store.usgs.gov/ Zobel, E. A. (2014). Angle Measurement:
Degrees, Minutes, Seconds [Photograph]. Retrieved April 20, 2015,
from:
http://zonalandeducation.com/mmts/trigonometryRealms/degMinSec/degMinSec.htm
