What do "Flatland", "A Wrinkle in Time", and the surrealist paintings of Salvador Dali have in common? They all explore phenomena in spaces beyond the third dimesions, ideas that have fascinated and challenged mathematicians, physicists, philosophers, and artists for centuries. Only very recently, however, has it been possible to see and interact with objects in higher-dimensions using modern computer graphics. In this presentation, we will encounter representations of hypercubes, hyperspheres, Klein bottles, and other objects that can't be built in our space. What kinds of new mathematical insights will lie ahead?
Thomas Banchoff is a pioneer in using computer graphics to explore geometry beyond the third dimension. He was an undergraduate at the University of Notre Dame and he received his Ph.D. at the University of California, Berkeley, in 1964. He has been teaching at Brown University since 1967. In 1996, he received a national award for Distinguished Teaching from the Mathematical Association of America, and he served as president of the MAA in 1999 and 2000. He is the author of "Beyond the Third Dimension" and a new introduction to his favorite book, "Flatland".