Arbitrary Curves of Constant Width

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Both the circle and the Reuleaux triangle are examples of curves of constant width. Such curves, if fitted into a square, can rotate in constant contact with all four sides. Any triangle can serve as a template for a curve of constant width by putting three pairs of arcs of circles around it, centered at each of the three vertices, as shown by this Demonstration.

[more]

Barbier's theorem [1] proves that a curve with constant width 1 has a perimeter of π.

[less]

Contributed by: Ed Pegg Jr (January 2013)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Reference

[1] Wikipedia, Barbier's theorem.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send