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Field: Geometry
Image Created By: Wolfram MathWorld
Website: Wolfram MathWorld


Four different roulettes formed by rolling four different shapes through one fixed point.

Basic Description

Suppose you see a nickel rolling on the sidewalk. Imagine a pen traced the path path of one fixed point on the coin as it rolled. A curve would be created. This curve is called a roulette. The example is depicted below:

Cycloid animated.gif     

However, a roulette is not restricted to straight lines and circles. The rolling curve can range from a line to a parabola to a decagon. Similarly, the surface on which this curve rolls on does not have to be a line. It can be a parabola as well, or a circle, among many others. There are a few restrictions that apply:

  • The curve that is not rolling must remain fixed.
  • The point on the rolling curve must remain fixed.
  • Both curves must be differentiable.
  • The curves must be tangent at one point at all times.

There are numerous cases of different roulettes; the most common ones have been named. A few of these have been listed below:

A roulette is a curve traced by one single point on a shape as it rolls without slipping along another shape, curve, or line.

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Video of a man riding a bike with square-shaped wheels.

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