The Mathematical Association of America Maryland-District of Columbia-Virginia Section

On November 3-4, Hampden-Sydney College and Longwood University hosted the Fall 2006 MD-DC-VA Regional Meeting of the MAA.

• On Friday at Hampden-Sydney College, Eve Torrence of Randolph–Macon College gave the late afternoon workshop entitled Buckyballs and Mathematical Origami. Later that evening, Thomas Hull of Merrimack College delivered the banquet address, Origami Math and its Increasing Intersections.
• On Saturday at Longwood University, our two invited speakers were Betty Mayfield of Hood College, who spoke on Gerbert d'Aurillac and the March of Spain: A Guy in the Right Place at the Right Time, and John Osoinach of Millsaps College, who discussed Lying Oracles, Biased Coins, and Stanislaw Ulam.

Invited Addresses

Eve Torrence

Workshop: Buckyballs and Mathematical Origami

Abstract: A Buckyball is a representation of the chemical structure of carbon-60. It is also models the structure of a soccer ball. In this workshop we will discover some of the geometric properties of Buckyballs. We will learn how to build polyhedra using modular origami and how tools from graph theory and combinatorics can reveal properties of these solids.

Biographical Sketch: Eve Torrence received her Ph.D. in 1991 from the University of Virginia. She was a Clare Boothe Luce professor at Trinity College, Washington, D.C. from 1991 to 1994 and is currently an associate professor at Randolph-Macon College. She is the chair of the Maryland-District of Columbia-Virginia section of the MAA and a member of the Pi Mu Epsilon Council. She is the co-author, with husband Bruce Torrence, of The Student's Introduction to Mathematica, A Handbook for Precalculus, Calculus, and Linear Algebra (Cambridge, 1999). Her areas of interest include geometry, origami, and mathematics education. She also enjoys gardening, horseback riding and playing with her children and her Australian shepherd puppy.

Thomas Hull

Banquet Address: Origami Math and its Increasing Intersections

Abstract: Mathematical studies of origami (paper folding) have been enjoying growing attention over the past 5 years. Computational folding problems have found applications in protein folding, and engineering fields from nanotechnology to solar panels in outer space have turned to origami for assistance. Such attention had led to a deeper understanding of the various ways in which paper folding can be modeled mathematically. One surprise has been the sheer number of different branches of math that can be applied to origami. From geometry to abstract algebra to number theory to combinatorics, origami seems to crimp its way into everything. This talk will present a survey of the diverse field that is origami mathematics, with particular attention placed on recent discoveries of both old and new connections.

Biographical Sketch: Thomas Hull learned origami at age 8 from a hermit uncle, first glimpsed its connections to math while an undergraduate at Hampshire College, helped develop its theory while in grad school at the University of Rhode Island (where he fooled everyone by getting his Ph.D. in graph theory), and now teaches at Merrimack College in Massachusetts. He is considered a leading expert on origami mathematics as well as an accomplished paper folder. His PHiZZ unit has infected the fingers of procrastinators world-wide, and his Five Intersecting Tetrahedra model was voted by the British Origami Society as one of the top 10 origami models of all-time. He recently wrote a book, Project Origami (AK Peters), and he'll be one of the subjects of an upcoming documentary on origami (see the trailer at www.greenfusefilms.com). To see more about his work and folds, visit Tom's web page: http://www.merrimack.edu/~thull.

Betty Mayfield

Invited Address: Gerbert d'Aurillac and the March of Spain: A Guy in the Right Place at the Right Time

Abstract: Gerbert was a tenth century scholar and churchman who eventually was named Pope Sylvester II. In the Year 1000, he probably knew more mathematics than anyone else in Europe. We'll explore how that came to be.

Biographical Sketch: Betty Mayfield holds degrees in mathematics from the University of North Carolina at Greensboro and the University of Rhode Island. She has taught at Hood College since 1979, where she is currently professor and chair in the Department of Mathematics. Her research interests include underwater acoustics, mathematical pedagogy and its effects on young women, and the history of mathematics, especially Gerbert. She has served as newsletter editor, chair, and governor of this Section, and was the recipient of its 2001 Award for Distinguished Teaching.

John K. Osoinach, Jr,

Invited Address: Lying Oracles, Biased Coins, and Stanislaw Ulam

Abstract: At a casino operated by a clairvoyant oracle, gamblers place bets on the outcome of a flip of a coin. To assist them with their wagers, the oracle can predict the outcome, but lies occasionally. This talk will explore how to find the optimal strategy to outwit the oracle, if possible, and then discuss variants on this theme, including using a biased coin. Finally, we will compare this game to Ulam’s number-guessing game that he first proposed in his "Adventures of a Mathematician".

Biographical Sketch: John Osoinach earned his Ph.D. in 1998 at the University of Texas at Austin. While his main area of research is in low-dimensional topology, specifically the geometry and topology of 3-manifolds, John has supervised several undergraduates in research projects ranging from topology to the mathematics of social choice. At MathFest in 2006, he was awarded the Carl B. Allendoerfer award for the article “Outwitting the Lying Oracle”, co-authored with Robb Koether of Hampden-Sydney College. He is currently an Assistant Professor of Mathematics at Millsaps College in Jackson, Mississippi.