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.
1st - torus. Shoot along any direction.
2nd - shoot diagonally right and up.
3rd - teabag, shoot diagonally up and left.
4th - straight to right
First and third can be created out of a sheet of paper.