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Broad Topics > 3D Geometry, Shape and Space > Non Euclidean Geometry

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Curvature of Surfaces

Age 16 to 18

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

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Pythagoras on a Sphere

Age 16 to 18 Challenge Level:

Prove Pythagoras' Theorem for right-angled spherical triangles.

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When the Angles of a Triangle Don't Add up to 180 Degrees

Age 14 to 18

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. . . .

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How Many Geometries Are There?

Age 16 to 18

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