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SESSION TWO: 3:15-5:30pm

NEIL SLOANE on “The Music of Quadratic Forms” Sloane, an AT&T Fellow, Member National Academy of Engineering, etc., is the creator of the On-Line Encyclopedia of Integer Sequences. He has recently been experimenting with different ways to study number sequences, both graphically and musically. He will show some remarkable pictures and play computer-simulated piano sequences that are related to Coxeter's work on quadratic forms. “There are thousands of notes and they go by VERY fast,” he says. Sloane will also display a sequence, discovered by Bernardo Recamán Santos, that is so difficult to decipher that it has been described as "How to Recamán's Life."

JOHN CONWAY on “The Four Dimensional Polytopes” Conway, the discoverer of surreal numbers and the John Von Neumann Professor of Mathematics at Princeton, considers himself an honorary student of Coxeter’s. And he is considered by many to be Coxeter’s spiritual successor as a geometer. During his university days at Cambridge, Conway was known to walk around wearing a helmet, a homemade contraption with army surplus periscopes screwed onto it which nearly allowed him to see in four spatial dimensions. He will speak on 4-dimensional polytopes. And he will tell the story of how Coxeter once tried to kill him with a problem pertaining to the rotational polyhedral groups and Coxeter groups, which resulted in a theorem that Conway now calls, “The Murder Weapon.”

TONY ROBBIN on "Coxeter, Hyper-Tessellations, and Quasicrystals" Robbin, based in New York, is pioneer in the computer visualization of 4-dimensional geometry. He has created large-scale quasicrystal sculptures in Denmark and the United States. Robbin is the author of Engineering a New Architecture and Shadows of Reality (both YUP). Following in the path of many geometers and artists the world over, Robbin wrote to Coxeter to ask a question. "In 1982, I had a question about tessellations of hypercubes," said Robbin, "and I still have the letter he wrote back. Coxeter made it all very clear to me." The resulting insights generated the mural size painting Fourfield, and the computer program HYPERS, which he will show, that displays nine tessellated hypercubes rotating in four- dimensional space.

MARC PELLETIER on “Coxeter’s Model Maker, Paul Donchian” Pelletier, a sculptor from Boulder, Colorado, who built the Conway and Coxeter 120-cells, and five others, will speak about Paul Donchian, whose

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