Sorry if this ends up being a naive question, but I have just a little conundrum. I'm dealing with curves in(adsbygoogle = window.adsbygoogle || []).push({}); R^{2}and the Gauss-Bonnet theorem is a very useful result with what I'm currently doing, what with Gaussian curvature of a flat surface being zero, which is all fine

http://mathworld.wolfram.com/Gauss-BonnetFormula.html

To proceed with my problem, I need to show that the geodesic curvature of a curve inR^{2}is the same as the standard curvature of it. I can sort of understand how it is the case from its definition but can'tshowit, if you know what I mean.

Thanks for all the help guys x

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Geodesic Curvature of a curve on a flat surface

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**