From Math Images
Revision as of 10:53, 28 June 2012 by Rlw82 (talk | contribs)
Jump to: navigation, search

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


Four different roulettes formed by rolling four different shapes and tracing a fixed point on each of these shapes.

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:

Cycloid animated.gif

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.


Interesting Application of the Concept

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 and the rolling curve does not need to be a circle but can be a polygon with sharp edges.

Below are a few examples of this concept:

Click to stop animation.
Click to stop animation.

It is easy to imagine a nickel rolling on the floor, but how can we imagine a square rolling a on a bumpy road? Professor Stan Wagon of Macalester College created a square-wheeled tricycle and demonstrated that it is possible for square wheels to work. Below is a short video that shows how this tricycle works. For more information go to Macalester Math and Science

EmbedVideo does not recognize the video service "tubechop".

Teaching Materials

There are currently no teaching materials for this page. Add teaching materials.


If you are able, please consider adding to or editing this page!

Have questions about the image or the explanations on this page?
Leave a message on the discussion page by clicking the 'discussion' tab at the top of this image page.