Rivaling the logarithmic spiral in elegance is the cycloid, the curve traced by a point on the rim of a circle that rolls along a straight line without slipping (right). The cycloid is characterized by its arcs and cusps, with each cusp marking the instant when the point on the wheel's rim reaches its lowest position and stays momentarily at rest. The cycloid has a rich history. In 1673, the Dutch physicist Christiaan Huy-gens (1629-1695) solved one of the outstanding problems that had intrigued 17th-century scientists: to find the curve down which a particle, moving only under the force of gravity, will take the same amount of time to reach a given final point, regardless of the initial position of the particle. This problem is known as the tautochrone (from the Greek words meaning "the same time").
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