## Stream: Is there code for X?

### Topic: Pythagoras' Theorem

#### Kevin Buzzard (Aug 23 2020 at 14:36):

Probably some differential geometers think that Pythagoras' theorem is $ds=\sqrt{dx^2+dy^2}$ in some abstract origin-less affine plane. Can we state something which means something like this? One could prove that $dx^2+dy^2$ was rotation-invariant (and reflection invariant, hence an invariant of the affine plane. @Joseph Myers you probably understand what I'm trying to understand here.

#### Patrick Massot (Aug 23 2020 at 14:45):

We already have affine spaces and it doesn't require being a differential geometer to think affine geometry doesn't need an origin.

#### Kevin Buzzard (Aug 23 2020 at 17:02):

But there's some content to the statement that the integral of ds from 0 to (a,b) is sqrt(a^2+b^2) right?

Last updated: May 16 2021 at 05:21 UTC