Non-Euclidean geometry

This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.

An account of how axioms underpin geometry and how by changing one axiom we get an entirely different geometry.

This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the triangle.

How do we measure curvature? Find out about curvature on soccer and rugby balls and on surfaces of negative curvature like banana skins.