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Conventional wisdom holds that the shortest distance between two points is a straight line.
While this is true, it may surprise you to discover that the fastest route between two points is not necessarily that hallowed straight line. If, as a ski coach, you think your racers can turn in faster times by taking a straight line between gates, you may be interested in a study I conducted that showed that the fastest line between two points on a ski slope is very often a cycloid curve. This theory, first observed by the Swiss scientist Johan Bernoulli in 1696, holds that the path of a particle sliding without friction from A to B under the force of gravity is not a straight line, but a cycloid curve. In fact, the calculus of variations had its beginnings in the solutions to this very brachistochrone problem. The experiment was performed on a 30 to 40-degree salted slope at Squaw Valley Ski Resort in April 1988 with skilled skiers and sophisticated timing equipment.