# Curves and Surfaces of Constant Width

Curves of constant width are useful for noncircular coins. As the number of sides increases, these curves quickly become more like disks and less like Reuleaux triangles. The curves here are defined using a simple support function: for an odd integer, .
To preserve convexity, is needed. Support functions have a central role in the definition of sets of constant width; for example, in the Eggleston (1952) proof of the Blaschke–Lebesgue (1914) theorem, the Reuleaux triangle is the planar set of constant width of minimal area.

### DETAILS

Rotating a curve of constant width about an axis of symmetry creates a surface of constant width [1, p. 196], but there are other kinds of surfaces of constant width. There are curves of constant width without an axis of symmetry [2].
References
[1] J. Bryant and C. Sangwin, How Round Is Your Circle?, Princeton, NJ: Princeton University Press, 2008 pp. 188–226.
[2] A. Bogomolny. "Star Construction of Shapes of Constant Width." (Apr 16, 2013) www.cut-the-knot.org/Curriculum/Geometry/CWStar.shtml.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.