Perimeter of a Reuleaux TriangleDate: 04/15/2001 at 09:49:51 From: deborah crisp Subject: Perimeter of a Reuleaux triangle How can I find perimeter of a Reuleaux triangle of width d? Is the formula circumference = pi times width (d)? This seems too simple. Date: 04/17/2001 at 14:26:30 From: Doctor Douglas Subject: Re: Perimeter of a Reuleaux triangle Hi Deborah, and thanks for writing. Yes, it does seem simple, but there is a theorem that states that all curves of constant width d have the same perimeter, pi*d: Barbier's theorem. You can verify this theorem directly for the Reuleaux triangle. Suppose that the diameter of the Reuleaux triangle is d. Each side of the base equilateral triangle has length d. Then the perimeter of the Reuleaux triangle is composed of three circular arcs, each of which has arc length equal to s = radius * subtended_angle = d * pi/3 angle is measured in radians and the total perimeter is S = 3*s = d*pi I hope this helps answer your question. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/ |
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