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.

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.