"Beyond the Third Dimension:
From `Flatland' to Internet Hypergraphics"
Interactive computer graphics makes it possible for the first time to experience direct visual contact with one of the most fascinating and challenging mathematical worlds: The Fourth Dimension. More than a hundred years ago, a remarkable book, "Flatland", laid out the challenge, and only now are we able to view and manipulate the objects in four-dimensional space. The Fourth Dimension--It's not just time anymore.
Prof. Banchoff will present computer generated slides and videos to illustrate the ways that the fourth dimension has inspired not only mathematicians and physicists, but also philosophers, writers, and surrealist artists. Also included in the presentation will be a trip to a virtual art gallery filled with surfaces "beyond the third dimension."
Singularities of Projections of Surfaces
into the Plane and Three-Space
Sunday, April 25, 1999
1:30 - 3:00 p.m.
Siemans Hall 128
Post-colloquium tea and reception from 3:15 - 3:45 p.m.,
Basement of the Library Foyer
Professor Banchoff will discuss some theorems about singularities of
projections of surfaces into the plane and three-space. Using interactive
computer graphics Professor Banchoff will illustrate that the way we do
mathematics and the way we communicate it to our students and our colleagues
is changing daily. Most of the content of the lecture will be accessible
to anyone who has completed at least 3 semesters of calculus and linear
Professor Banchoff is the author of over 50 research articles
and of three books, Introduction to Flatland for Princeton U Press,
the Third Dimension, Scientific American Library 1990, 1996 , and Linear
Algebra Through Geometry, Springer-Verlag, revised and expanded second
edition, Springer-Verlag (1991). His film, "The Hypercube", 1978,
won the Prix de la Recherche Fondementale at the Brussells Festival of
Scientific and Technical Films.
Professor Banchoff is currently the president of the Mathematical Association of America.