Egg-ovoid rolling down an inclined plane - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T05:32:58Z http://mathoverflow.net/feeds/question/111418 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/111418/egg-ovoid-rolling-down-an-inclined-plane Egg-ovoid rolling down an inclined plane Joseph O'Rourke 2012-11-04T01:21:44Z 2012-11-04T01:21:44Z <p>I am seeking a mathematical analysis of an egg-ovoid rolling down an inclined plane, for pedagogical reasons. It is well-known folk lore that the shape of an egg prevents it from rolling away from the mother's nest, e.g., the article "Why are eggs egg-shaped?" (<a href="http://www.bigsiteofamazingfacts.com/why-are-eggs-egged-shaped-and-how-does-the-ovoid-shape-of-an-egg-prevent-it-from-rolling-out-of-the-nest" rel="nofollow">link</a>), or, a bit more formally, "The Mathematics of Egg Shape" (<a href="http://www.osaka-ue.ac.jp/zemi/nishiyama/math2010/egg.pdf" rel="nofollow">PDF download</a>) by Yutaka Nishiyama, from which I copied this figure (and the one below): <br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="http://cs.smith.edu/~orourke/MathOverflow/EggInclinedPlane.jpg" alt="Egg Fig"><br /> If anyone has seen a mathematical analysis of this phenomenon, more precise than observing that an egg-ovoid fits inside a cone, and a cone rolls a circular arc, I would appreciate a pointer. Thanks! <br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="http://cs.smith.edu/~orourke/MathOverflow/EggInCone.jpg" alt="Egg Fig"><br /></p>