Rolling with Reuleaux
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Ivars Peterson (MathLand)  
Why is the cover of a manhole round? The usual answer is that a circular lid, unlike a square or hexagonal cover, won't fall through the opening. The circle works because it has a constant width, defined as the distance between a pair of parallel lines touching the curve on opposite sides. For a circle, the width is simply the circle's diameter. However, the circle isn't the only curve of constant width. There is actually an infinite number of such curves, any one of which could form a manhole lid... The simplest such curve is known as the Reuleaux triangle... It's possible to construct a curve of constant width not only from an equilateral triangle but also from any polygon with an odd number of sides.  


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Math Topics:  Conic Sections and Circles 
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