While watching Shaun White win the gold medal in the "half-pipe" snowboarding event at the Olympics yesterday (on TV), it occurred to me that the best cross section for the half-pipe would be the cycloid. The brachistochrone property of the cycloid should allow the snowboarder/skateboarder to do stunts, each of which take approximately the same time & thereby set up a better rhythm. I did some searching on the web, and discovered that the current halfpipe curve has evolved from a true semicircle to a flat area with two quarter circle "corners". So it appears that the "half-pipe" may eventually evolve into a cycloid. Regardless of the suggestions in the references below about the bottom of the half-pipe being flat, the actual contour of the snow in the Torino half-pipe appears to me to be much more like a cycloid. I guess a question for the DIY crowd would be how to describe to your son/nephew/grandson the easiest way to construct a proper cycloid without building a huge wheel. Is there a way to construct a large cycloid using strings & pegs, etc., in a manner analogous to constructing an ellipse? (I guess this discussion provides one answer to high school kids who ask why anyone would want to study math.) http://en.wikipedia.org/wiki/Half-pipe http://www.abc-of-snowboarding.com/snowboardinghalfpipe.asp http://mathworld.wolfram.com/Cycloid.html