Derive Circumference of a Circle

Discussion in 'Other Pre-University Math' started by nycmathguy, Jul 7, 2022.

1. nycmathguy

Joined:
Jun 27, 2021
Messages:
5,386
420
Derive the formulas C = d•pi and C = 2r•pi.

nycmathguy, Jul 7, 2022

2. MathLover1

Joined:
Jun 27, 2021
Messages:
2,989
2,883
by the definition of pi (π) is the circumference c of any circle divided by its diameter d

Put as an equation, pi is defined as π=c/d
Rearranging this to solve for c we get c=π*d

The diameter of a circle is twice its radius, so substituting 2r for d
c=2π*r

MathLover1, Jul 7, 2022
nycmathguy likes this.

3. nycmathguy

Joined:
Jun 27, 2021
Messages:
5,386
420
Is that all it takes to derive the circumference of a circle?

nycmathguy, Jul 7, 2022
4. MathLover1

Joined:
Jun 27, 2021
Messages:
2,989
2,883
yes

MathLover1, Jul 7, 2022
nycmathguy likes this.

Joined:
Jun 27, 2021
Messages:
5,386