This is posted for Tarin Bross, who's a Swarthmore student posting from the Conference this week in Albany, NY.
Hello, my name's Tarin Bross. I've been attending the Artnding the Art and Math conference at the State University of New York (SUNY) at Albany, NY. As many of the introductory speakers indicated, both art and mathematics use order, structure, and form to explore characteristics of nature and reality. Changes in art often accompany changes in mathematical thought; for example, numerous artists have cited the introduction of alternative geometries other than Euclidean as influential to their work. This conference was formed to bring together individuals interested in both art and/or math who wish to understand the relationships and interactions of the two areas. Following the suggestions of Prof. Klotz, I thought I'd pass along some interesting tidbits from the conference that are able to be described easily and are appropriate for the Geometry Forum.
Will Webber, a member of the math department at the University of Washington in Seattle, WA, had a display of a large number of monovalent, monohedril toroidal polyhedra. All of these multifaceted tori are folded out of a single sheet of paper and all of the faces are congruent (monohedril) and there are 6 faces at each vertex (monovalent). A few of the tori appear simple enough to be useful as a visualization tool in the classroom.
Dick Termes, who many of you may know as the creator of Termespheres gave a talk and a beautiful slide presentation of his work. Termes does paintings and drawing on spheres (and other shapes such as pyramids and various polyhedra). Using 6-point perspective, he is able to transfer all the space around an individual (say a room) onto the sphere. This gives an amazingly accurate representation of your surroundings. He argues that spherical geometry (what he call this process) is the best way to represent visual space and the entire environment surrounding you.
John Horton Conway, from Princeton, gave a riveting talk on symmetry. He gave an explanation of some ideas about symmetry: for example, he explained orbifolds. Orbifolds are ways of representing symmetric objects by "dividing out" the symmetry of the object. Oversimplifying even further, an orbifold is the building block of our object such that you can produce the entire object you are interested in by replicating and gyrating the orbifold. This can be a useful tool for understanding an object's symmetry.
Look for more of Tarin`s reports of conference proceedings next week.
Annie Fetter | The Geometry Forum | Voice: 215 328-8225 Project Coordinator | Swarthmore College | 800 756-7823 firstname.lastname@example.org | Swarthmore PA 19081 | Fax: 215 328-7824