Bactra Review `
` ` ` Geometrical Methods of Mathematical Physics

Consider the North Pole and the South Pole of a globe of radius *R.* Normally, the distance between them is 2*R*, in accordance with the Pythagorean formula. If you are constrained to paths on the surface of the sphere, however, the shortest distance is half a great circle, *(pi)R.* In fact, the shortest path between any two points is longer than it would be if one could leave the sphere.