Curve of constant width: Difference between revisions

Revision as of 03:12, 25 January 2022

Revision as of 19:39, 25 January 2022

Line 1:

{{good article}}

{{short description|Shape whosewith width is independent of orientation}}

[[File:Reuleaux supporting lines.svg|thumb|Measuring the width of a [[Reuleaux triangle]] as the distance between parallel [[supporting line]]s. Because this distance does not depend on the direction of the lines, the Reuleaux triangle is a curve of constant width.]]

In [[geometry]], a '''curve of constant width''' is a [[simple closed curve]] in the [[plane (geometry)|plane]] whose width (the distance between parallel [[supporting line]]s) is the same in all directions. The shape bounded by a curve of constant width is a '''body of constant width''' or an '''orbiform''', the name given to these shapes by [[Leonhard Euler]].{{r|euler}} Standard examples are the [[circle]] and the [[Reuleaux triangle]]. These curves can also be constructed using circular arcs centered at crossings of an [[arrangement of lines]], as the [[involute]]s of certain curves, or by intersecting circles centered on a partial curve.