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
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.