During the 1995 Summer Institute at The Geometry Center, a team of undergraduates, middle and high school mathematics teachers and Center staff developed curriculum materials supporting The Shape of Space video. The team developed a comprehensive curriculum, covering many areas related to the video. The following materials were selected for distribution based on their direct relevence to understanding the video itself.
The computer animation Outside In 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. Through a combination of dialogue and exposition accessible to anyone who has some interest in mathematics, Outside In builds up to the grand finale: Bill Thurston's "corrugations" method of turning the sphere inside out.
Not Knot is a guided tour into computer-animated hyperbolic space. It proceeds from the world of knots to their complementary spaces -- what's not a knot. Profound theorems of recent mathematics show that most known complements carry the structure of hyperbolic geometry, a geometry in which the sum of three angles of a triangle always is less than 180 degrees.
