Why is circumference equal to 2 times Pi times r?

Answer 1

Circumference = pi times diameter

or

Circumference= two x pi x radius.

Now remember the diameter of a circle is the straight line from one edge of the circle, through the centre to the opposite edge.

The straight line from the edge to the centre is the radius, and then from the centre to the opposite edge is another radius. So the diameter is the length of two radii.

Algebraically express as d = 2r.

So Algebraically

C = pi*d

Substituting the 'd' for '2r'

C = pi2r

However in algebra coefficient numbers are expressed to the left. Hence

C = 2pir

Why 'C' is this expression I would have to go into some 'very heavy' differential calculus.

Suffice it to say, the ancients found that the circumference traced by a donkey/mule driving water out of well was directly proportional to the diameter, twice the length of the tether(2 radii).

From this they discovered that for however long the the tether and the circumference were. they had a constant of proportion

C directly related to diameter.

This is equated to

C = kd

And

k = C/d , which was founf to be 3.141592..... which now call 'pi'. for any sized circle.

So today in school you learn

C = pi d

or

C = 2 pi r

And for circular area(A)

A = pi r^(2)

The 'pi' youare given in school is proabably 3.14 , 3.1416 or 22/7 . However, these values are Approximatons, because 'pi' is an irrational number.

Hope that helps!!!!!!

Answer 2

circumference=pi circumference=pi circumference=pi