- Four different roulettes formed by rolling four different shapes and tracing a fixed point on each of these shapes.
Suppose you see a nickel rolling on the sidewalk. Imagine a pen traced the 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:
However, a roulette is not restricted to straight lines and circles. The rolling object can range from a point on a line to a parabola to a decagon to anything. Similarly, the surface on which this curve rolls 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.
A More Mathematical Explanation
There are numerous cases of different roulettes; the most common ones have been named. A few of these [...]
There are numerous cases of different roulettes; the most common ones have been named. A few of these have been listed below:
Interesting Application of the Concept
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