On NPR's Saturday Weekend Edition, they did a story with "Math Guy" Keith Devlin. He described a recent (last year) proof that, if the slope of the ground is at most about 35 degrees (actually, ArcTan[1/Sqrt[2]]), then you can balance a wobbly table by rotating it. (This assumes a mathematically perfect table, with the ground being a continuous function of x and y). Links: Audio of NPR story: http://www.npr.org/templates/story/story.php?storyId=7466072 Keith Devlin's website with a description: http://www.maa.org/devlin/devlin_02_07.html Technical article: http://arxiv.org/PS_cache/math/pdf/0511/0511490.pdf Scientific American article: http://www.sciam.com/article.cfm?articleID=5B1CAEBA-E7F2-99DF-3CD6B81A81B511... Mathematica animated movie: http://www.maths.monash.edu.au/~bpolster/table.mov