problem

### Weird universes

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

problem
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Weird universes

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

problem
###
Torus patterns

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

problem
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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.

problem
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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.

problem
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Flight Path

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

article
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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.

article
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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.

article
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How many geometries are there?

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

article
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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.