Not Knot - Outside In

This package includes a DVD of two award-winning computer animations of mathematical concepts and theorems, as well as supplementary material.Not Knot This animation is a guided tour into computer-animated hyperbolic space. It proceeds from the world of knots to its complementary space, what’s not a knot. Profound theorems show that most knot complements carry the structure of hyperbolic geometry. The video shows the geometry of the knot complement, the space around the knot, changing into hyperbolic space, and then you see what it is like to “fly through” hyperbolic space. Each new viewing will produce questions or answers to previous questions. You may find the answers to your queries in the supplement. It leads you through the video script and provides explanations for many puzzling questions that have been asked by students and mature mathematicians alike. You will be rewarded with a better understanding of how mathematicians see and explore space.Outside In This video explains the amazing discovery, made by Steve Smale in 1957, that a sphere can be turned inside out by means of smooth motions and self-intersections. Stunning computer animation combined with accessible dialogue and exposition builds up to the grand finale— Bill Thurston’s “corrugations” method of turning the sphere inside out.The accompanying four-color booklet, Making Waves, includes a transcript of the movie’s lively dialogue and expands on the explanations provided in the film. For the mathematically adventurous, the booklet also includes an article by Bill Thurston himself, on how the method of corrugations can be applied to similar problems in any dimension.