The circumference and Area of a circle

The circumference and Area of a circle

http://hench-maths.wikispaces.com

Diameter

Radius

centre

What is the formula

relating the circumference

to the diameter?

People knew that the circumference is about 3 times the diameter but they wanted to find out exactly.

C = ? x d

C ≈ 3 x d

This means APPROXIMATELY EQUAL TO

http://illuminations.nctm.org/ActivityDetail.aspx?ID=116

Investigating the relationship between the circumference of a circle and its diameter?

Click on the link below and read the instructions.

Use the applet to create circles with different diameters.

Your goal is to discover the mystery number in the formulae by

dividing the circumference by the diameter for each circle.

The mystery ratio• What value did you find for the ratio?

3.1-3.2 is pretty good

3.14 is very good and close to the true value

For most circumstances we say

Circumference ≈ 3.14 x diameter

What is the true value of this mystery ratio?????

Early Attempts

Egyptian Scribe Ahmes. in 1650 B.C. said C≈3.16049 x d

Archimedes, said C ≈3.1419 x d

Fibonacci. In 1220 A.D. said C≈3.1418xd

What is the value of the number that multiplies the

diameter to give the circumference????

The exact true value is……………

UNKNOWN!!

An approximation to π

π≈3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609................forever….

Videos on Circles•http://www.youtube.com/watch?v=eiHWHT_8WrE

•A Rap about circles

http://www.youtube.com/watch?v=fogehnFNDw0&feature=related

•Circle Song2

http://www.youtube.com/watch?v=lWDha0wqbcI&feature=related

What about the AREA of a circle?2r

2rr

First consider a square

The area of this square

in terms of r is

A= 2r x2r = 4r2

What about the AREA of a circle?2r

2r

Now consider a circle inside the square

The area of the circle must be less than the are of the square

A < 4r2

r

Area = ? xr2

Finding a formulae for the area of a circle

C= πd or C=2πr

Semi-circle=πr

πr

r

Area of Rectangle= Base x Height

Area = πr x r

Area =πr2

The Area and Perimeter of a CircleA circle is defined by its diameter or radius

Diameter

radi

usThe perimeter or circumference of a circle is the distance around the outside

The area of a circle is the space inside it

The ratio of π (pi)diameter

ncecircumfere

π is an irrational number whose value to 15 decimal places is π = 3.14159265358979.... We usually say π≈3.14The circumference is found

using the formula

C=π d or C= 2πr (since d=2r)

The area is found using the formula

A=πr2

The Area and Perimeter of a CircleA circle is defined by its diameter or radius

Diameter

radi

usThe perimeter or circumference of a circle is the distance around the outside

The area of a circle is the space inside it

The ratio of π (pi)diameter

ncecircumfere

π is an irrational number whose value to 15 decimal places is π = 3.14159265358979.... We usually say π≈3.14The circumference is found

using the formula

C=π d or C= 2πr (since d=2r)

The area is found using the formula

C=πr2