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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.

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.

Flight Path

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

Over the Pole

Age 16 to 18
Challenge Level

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.