the circumference and area of a circle
TRANSCRIPT
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