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????
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
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