The History of Curvature from Aristotle to Gauss

Good introduction to the Curvature of Surfaces

A course on differential geometry

A very nice presentation on curvature of space

A beautiful relationship between circumscribed polygons and total curvature.

Overview of different forms of curvature including

• Gaussian Curvature (intrinsic to the surface)
• Mean Curvature
• Fundamental Forms

Read about how an ant on a surface in R³ would measure the intrinsic curvature of his universe.

Metrics, maps and the curvature of space.

General Relativity curvature, Einstein's equations.

Pictorial guide to Special and General Relativity.

Summary of formulae for arclength and curvature

1. Can we tell if we live in a "flat" space or a "curved" space?
2. If space is curved, is it postively curved (e.g. part of a sphere) or negatively curved (e.g. part of a saddle)