Great Circle Routes

Since the earth is spherical in shape, the shortest distance between any two points on the globe lies along its circumference. There are an infinite number of great circles of equal length running around the globe, e.g. the circle formed by the Greenwich Meridian and the 180 degrees meridian; the circle formed by the 130 degrees west and 50 degrees east meridians. Of the lines of latitude, only the equator is a great circle.
When drawn on a globe great circles appear as straight lines, but when they are drawn on flat maps of the world they may not appear so. In fact on many maps great circles appear curved and routes along a straight line joining two places. This is an illusion created by the distortion of the shape of the earth to allow it to be drawn on a flat map.
Modern aircrafts follow routes along sections of great circles for speedy long-distance flights and thus cut down flying time. But it is not always possible to follow great circle routes. Firstly, air routes must link numerous cities and thus planes proceed in short 'hops' from place to place; secondly, it may be impossible to fly along great circles for political reasons if some countries forbid the use of their air-space; thirdly, air routes tend to follow the land in case of accidend and rarely fly for long distances over the sea. However, where long distances have to be covered over uninhabited regions, great circle routes are the quickest. They are therefore used in crossing polar regions. Some of the major great circle routes over the pole include that from London to Vancouver or Los Angeles, that from Tokyo to Stockholm and that from Tokyo to Mexico City. Polar routes are not only quicker but also relieve air-traffic congestion on the very crowded conventional routes.