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There are **10** NRICH Mathematical resources connected to **Non-Euclidean geometry**, you may find related items under 3D geometry, shape and space.

Problem
Primary curriculum
Secondary curriculum
### Weird Universes

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Torus Patterns

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

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Curvature of Surfaces

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

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Over the Pole

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Spherical Triangles on Very Big Spheres

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pythagoras on a Sphere

Prove Pythagoras' Theorem for right-angled spherical triangles.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Flight Path

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

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### When the Angles of a Triangle Don't Add up to 180 Degrees

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.

Age 14 to 18

Article
Primary curriculum
Secondary curriculum
### How Many Geometries Are There?

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

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### Geometry and Gravity 1

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.

Age 11 to 18