1. The circumference and Area
of a circle

2. What is the
formula
relating the
circumferenc
e to the centre
diameter? Diameter

3. C=?xd
People knew that the circumference is about 3
times the diameter but they wanted to find out
exactly.
C≈3xd
This means APPROXIMATELY EQUAL TO

4. 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.
Roll the circles on the number line to measure the circumference.
Your goal is to discover the mystery number in the formulae by
dividing the circumference by the diameter for each circle.
If you measure and divide corectly you should always get the same value
for the ratio circumference/diameter

5. 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?????

6. 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????

7. The exact true value is……………
UNKNOWN!!


8. An approximation to π
π≈3.141592653589793238462643383279502884
19716939937510582097494459230781640628
62089986280348253421170679821480865132
82306647093844609550582231725359408128
48111745028410270193852110555964462294
89549303819644288109756659334461284756
48233786783165271201909145648566923460
34861045432664821339360726024914127372
45870066063155881748815209209628292540
91715364367892590360011330530548820466
521384146951941511609................forever….

9. Videos on Circles
•http://www.youtube.com/watch?v=eiHWHT
_8WrE
•A Rap about circles
http://www.youtube.com/watch?v=fogehnFN
Dw0&feature=related
•Circle Song2
http://www.youtube.com/watch?v=lWDha0w
qbcI&feature=related

10. What about the AREA of a circle?
2r
First consider a square
r The area of this square
2r
in terms of r is
A= 2r x2r = 4r2

11. What about the AREA of a circle?
2r Now consider a circle inside the square
The area of the circle must be less than
the area of the square
r
2r
A < 4r2
Area = ? xr2

12. Finding a
formulae for the
area of a circle

13. C= πd or C=2πr
Semi-circle=πr
πr
r

14. Area of Rectangle= Base x Height
Area = πr x r
Area =πr2

15. The Area and Perimeter of a Circle
A circle is defined by its diameter or radius
The perimeter or circumference of a circle
is the distance around the outside
The area of a circle is the space inside it
Diameter
circumference
The ratio of  π (pi)
diameter
π is an irrational number whose value to 15 decimal places is
π = 3.14159265358979.... We usually say π≈3.14
The circumference is found The area is found
using the formula using the formula
C=π d or C= 2πr (since d=2r) A=πr2

16. The Area and Perimeter of a Circle
A circle is defined by its diameter or radius
The perimeter or circumference of a circle
is the distance around the outside
The area of a circle is the space inside it
Diameter
circumference
The ratio of  π (pi)
diameter
π is an irrational number whose value to 15 decimal places is
π = 3.14159265358979.... We usually say π≈3.14
The circumference is found The area is found
using the formula using the formula
C=π d or C= 2πr (since d=2r) C=πr2