# Curvature and Tangential angle

1. Jun 30, 2010

### ForMyThunder

In Differential Geometry by Heinrich Guggenheimer (if you have the book, the proof I am asking about is Theorem 2-19), he gives the angle between a chord through points s and s' and the tangent at s, as the integral of the curvature (with respect to arc length) from s' to s. I'm not sure how he got this, because I thought that the integral of curvature gave the angle between the tangent and the x-axis. Or maybe I'm not understanding something.

2. Jun 30, 2010

### Eynstone

It should be the angle between the tangents at the endpoints. (You can, of course, calculate the slope of the chord thereon).

3. Jul 3, 2010