There are **10** NRICH Mathematical resources connected to **Non Euclidean Geometry**, you may find related items under 3D Geometry, Shape and Space.

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Consider these weird universes and ways in which the stick man can shoot the robot in the back.

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How many different colours would be needed to colour these different patterns on a torus?

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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Two places are diametrically opposite each other on the same line of latitude. Compare the distances between them travelling along the line of latitude and travelling over the nearest pole.

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Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

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Prove Pythagoras' Theorem for right-angled spherical triangles.

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Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

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. . . .

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