A Rolling Reuleaux Triangle

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A Reuleaux triangle is constructed from an equilateral triangle by joining each pair of vertices with a circular arc centered at the third vertex (each radius is equal to the side length of the triangle).

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The width of a figure in a given direction is the smallest width of all the strips perpendicular to that direction that contain the figure. For instance, the width of a unit square varies from 1 to as the direction changes from 0° to 45°.

Among the many interesting geometric features of a Reuleaux triangle is that (like a circle) it is a curve of constant width, as illustrated here. As the triangle rolls along the axis, its width remains constant. However, the center of the figure, whose path is shown in red, does not remain level as the triangle rolls.

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Contributed by: Chris Boucher (March 2011)
Open content licensed under CC BY-NC-SA


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