An account of how axioms underpin geometry and how by changing one axiom we get an entirely different geometry.
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.
Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.
Simon from Elizabeth College, Guernsey and
Andrei from Tudor Vianu National College, Romania have both solved
this problem and both solutions are used below.