2003 Section Meeting

Invited talks

Jim Tattersall, Providence College

Three Mathematical Vignettes: Millennial, Promiscuous, and Nyctaginaceous

Abstract: In the first century A.D., the Introduction to Arithmetic, by Nicomachus of Gerasa and Mathematics Useful for Understanding Plato by Theon of Smyrna were one the few sources of knowledge of formal Greek arithmetic in the Middle Ages. The books are philosophical in nature, contain few original results, and no formal proofs. They abound, however, in intriguing observations in number theory. We discuss and extend some of the number theoretic results found in these ancient volumes. Secondly, we discuss the promiscuous scheme proposed by John Colson, Lucasian Professor of Mathematics at Cambridge, for avoiding the use of the digits 6,7,8, and 9. Finally, we mention, Louis Antoine de Bougainville, mathematician, explorer, and student of D'Alembert who wrote a sequel to L'Hospital's "Analyse des Infiniment Petits". Bougainville was present at the Battle of Quebec and when Cornwallis surrendered at Yorktown. He also circumnavigated the globe. We discuss some of the contents of his text book and recount several of his adventures.

Bill Lindgren, Slippery Rock University

The Most Interesting Natural Number

Abstract: We show that 23 (the favorite number of Michael Jordan and John Nash) is the most interesting of all natural numbers. The evidence includes joint work by the author, Peter Fletcher, and Carl Pomerance on symmetric and asymmetric primes.

Annalisa Crannell, Franklin & Marshall College

Math and Art: The Good, the Bad, and the Pretty

Abstract: Dust off those old similar triangles, and get ready to put them to new use in looking at art. We're going to explore the mathematics behind perspective paintings---a mathematics that starts off with simple rules, and yet leads into really lovely, really tricky mathematical puzzles. Why do artists use vanishing points? What's the difference between 1-point and 3-point perspective? What's the difference between a perspective artist and a camera? We'll look at all of these questions, and more. We'll solve artistic puzzles with mathematical theorems, using hands-on examples.