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       #Post#: 100--------------------------------------------------
       REULEAUX WHEEL
       By: eba95 Date: July 30, 2010, 6:11 am
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       Reuleaux Wheel
       A Reuleaux Triangle is a plump
       triangle with rounded edges, formed
       in the following way: take the three
       points at the corners of an
       equilateral triangle, and connect
       each pair of points by a circular arc
       centered at the remaining point.
       This triangle has some amazing
       properties. It is constant-width,
       meaning that it will hug parallel
       lines as it rolls. By rotating the
       centroid of the Reuleaux triangle
       appropriately, the figure can be
       made to trace out a square, perfect
       except for slightly rounded corners!
       This idea has formed the basis of a
       drill that will carve out squares!
       And, what do you think the ratio of
       its circumference to its width is?
       Amazing fact: it is PI!
       Presentation Suggestions:
       Have students think about why this
       figure is constant width.
       The Math Behind the Fact:
       There are many other convex,
       constant-width figures, such as the
       circle and various Reuleaux
       polygons, and they all satisfy the
       same ratio of circumference to
       width!
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