A cycloid is the curve formed by a fixed point on the edge of a wheel as the wheel rotates along the ground. The curve is given by the parametric equations
x = r (t - sin t),
y = r (1 - cos t)
where r is the radius of the wheel. If you take one arch of the graph and turn it upside down it forms a ramp with a special property: it is the fastest path for a ball rolling down from one point to another. A second interesting fact: if you do have a ramp in this shape, no matter where you start a ball rolling, it will always take the same amount of time to reach the bottom. The cool photo is from illum on Flickr.
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Related links:
Wikipedia entry for cycloid
YouTube video of a marble rolling down a cycloid ramp
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