Roulette
From Math Images
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=Variations= | =Variations= | ||
There are numerous cases of different roulettes; the most common ones have been named. A few of these are listed below: | There are numerous cases of different roulettes; the most common ones have been named. A few of these are listed below: | ||
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=== Trochoid === | === Trochoid === | ||
A '''trochoid''' is any roulette in which the fixed curve is a line and the rolling curve is a circle.When the fixed point is on the edge of the rolling circle, then the roulette is called a '''cycloid'''. If the point is inside the rolling circle, then the curve produced is called a '''curtate cycloid'''. If the point is on the outside of the rolling circle, then the curve produced is called a '''prolate cycloid'''. | A '''trochoid''' is any roulette in which the fixed curve is a line and the rolling curve is a circle.When the fixed point is on the edge of the rolling circle, then the roulette is called a '''cycloid'''. If the point is inside the rolling circle, then the curve produced is called a '''curtate cycloid'''. If the point is on the outside of the rolling circle, then the curve produced is called a '''prolate cycloid'''. | ||
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== Interesting Application of the Concept == | == Interesting Application of the Concept == | ||
{{Hide|1=The above roulettes are only a few of many different types of this curve. The main image of the page demonstrates that the fixed curve can be a [[Catenary|catenary]] and the rolling curve does not need to be a circle but can be a polygon with sharp edges. | {{Hide|1=The above roulettes are only a few of many different types of this curve. The main image of the page demonstrates that the fixed curve can be a [[Catenary|catenary]] and the rolling curve does not need to be a circle but can be a polygon with sharp edges. |
Current revision
Roulette |
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Roulette
- Four different roulettes formed by rolling four different shapes and tracing a fixed point on each of these shapes.
Contents |
Basic Description
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 all times.
In the example of the rolling nickel, we imagine that the point of the pen is somewhere on the edge of the nickel. However, this point does not have to be on the edge of the rolling object. It can be also be inside or outside, varying how the curve will look.
Variations
There are numerous cases of different roulettes; the most common ones have been named. A few of these are listed below:
Interesting Application of the Concept
Teaching Materials
- There are currently no teaching materials for this page. Add teaching materials.
References
- Weisstein, Eric W. "Roulette." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Roulette.html
- http://en.wikipedia.org/wiki/Roulette_(curve)
- http://www.geom.uiuc.edu/docs/reference/CRC-formulas/node34.html
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