2

Everybody know this formula,but why the relation between $C$ and $r$ is linear relation? Not $C=2πr^{0.99}$ or $C=2πr^{1.01}$how to prove it,what axiom is it based on?

PunkZebra
  • 1,595
Tom
  • 671
  • 1
    Well the statement $(\exists \pi \in \mathbb{R}, \forall C \in \text{ Circles }),C_{circumfrence} = 2\pi C_{radius}$ follows from basic understanding of how things scale in 2 dimensions (proportionality). This may as well be used to simply define $\pi$. – DanielV May 17 '14 at 17:47
  • 2
    Strange question for one of the greatest geometers of the 20th century to be asking. :) – Ted Shifrin May 17 '14 at 19:12

1 Answers1

1

As the rectification of the circle ultimately relies on triangulation, this follows from the corresponding proportionality for triangles, hence ultimately from the intercept theorem (not a single axiom).

Hagen von Eitzen
  • 374,180