What is the relationship between pi and circles?

Answer 1

'pi' is the constant of proportionality for ALL circles of whatever size. 'pi' has the values of 3.141592.... (to infinity). For school work pi = 3.14

For circle area A = pi r^2

circle circumference C = 2pi r = pi d

Volume of a sphere V = (4/3) pi r^3

Surface Area of a sphere SA = 4 pi r^2

The ancients before Classical Greece noticed that when an mule/donkey was tied to a centre pole (the radius) and was driven around the pole in a circle to drive up water (circumference) there was a constant ; pi = 3.14....

e.g. diameter 'd' = 2r = 10 and circumference = 31.4

Then C constant of proportionality d

Inserting the numbers

31.4 = constant X 10

constant = 31.4 / 10 = 3.14

This constant was named 'pi' ; the Classical Greek small case letter 'p', for proportionality. This constant held good for any circle of any size.

Hence we have C = pi d => C = 3.14 d further calculations gave us the Area as A = pi r^2 => A = 3.14 r^2

'pi' is an Irrational number. Casually this means the decimals go to infinity and there is no regular order in the digits. Your calculator may show pi = 3.141592654, but this is only an approximation. #

pi = 3.141592654...

Supa /dupa computers have calculated 'pi' to several billions of places and still going.

Answer 2

The circumference of a circle is pi times the diameter.

The area of a circle is pi times the radius squared.