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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.

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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.

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Flight Path

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

Over the Pole

Stage: 5 Challenge Level: Challenge Level:1

This problem affirms the idea that great circle distances on a sphere are the shortest distances. It prepares the way for more complicated calculations of distances between any two places on the globe.

See Flight Path.