On April 4-5, 2008, James Madison University and Eastern Mennonite University
hosted the Spring 2008 MD-DC-VA Section Meeting of the MAA. On Friday evening at
Eastern Mennonite University Carolyn Yackel of Mercer University gave a
workshop entitled Math Meets Reality-Realizing Some Mathematical Ideas in Knitting.
Elizabeth Theta Brown of James Madison University gave the Mid-Banquet slideshow and
Art Benjamin of Harvey Mudd College delivered the banquet address Mathemagics!
On Saturday, at James Madison University, Art Benjamin talked on
Combinatorial Trigonometry (and a method to DIE for).
That afternoon Susan Goldstine from St. Mary's College of Maryland will be giving a talk entitled
The Geometries of Escher. Judy Townsend exhibited her work entitled Organic Geometry.
Congratulations to Bruce Torrence of Randolph-Macon College, the 2008 recipient of the
John Smith Award for Distinguished College or University Teaching.
Our annual Undergraduate Student Conference was well attended, featuring student paper and poster
sessions and a Jeopardy competition hosted by Bud Brown of Virginia Tech.
Workshop: Math Meets Reality-Realizing Some Mathematical Ideas in Knitting
Beginning with an abstract mathematical myth of octagonal pants and
paper manipulatives, we go through stages of mathematical formalization
followed by translation to a knitting pattern that allows us to demystify the
myth and understand it as fact. In the process we develop an infinite number
of knitting patterns for hyperbolic space and for pants of various dimensions.
As time allows, other topics may be discussed.
Carolyn Yackel was educated at the University of Chicago (S.B.) and at
the University of Michigan (M.S., Ph.D.), where she trained as a commutative
algebraist. She's now an associate professor at Mercer University, where she
studies the implications of mathematics for fiber arts and vice versa--an
emerging field usually referred to as math and fiber arts. This subject brings
her much joy as it marries her two loves. She enjoys working both alone and
with her major collaborator, Sarah Marie Belcastro, with whom she recently
edited their first book, Making Mathematics with Needlework.
Harvey Mudd College
Banquet Address: Mathemagics!
Dr. Arthur Benjamin is a mathematician and a magician. In his
entertaining and fast-paced performance, he will demonstrate and
explain how to mentally add and multiply numbers faster than a
calculator, how to memorize 100 digits of pi, how to figure out
the day of the week of any date in history, and other amazing feats of
mind. He has presented his mixture of math and magic to audiences all
over the world.
Saturday Morning Address:
Combinatorial Trigonometry (and a method to DIE for)
Many trigonometric identities, including the Pythagorean theorem, have
combinatorial proofs. Furthermore, some combinatorial problems have
trigonometric solutions. All of these problems can be reduced to
alternating sums, and are attacked by a technique we call
D.I.E. (Description, Involution, Exception). This technique offers new
insights to identities involving binomial coefficients, Fibonacci
numbers, derangements, zig-zag permutations, and Chebyshev
Arthur Benjamin earned his B.S. in Applied Mathematics from Carnegie
Mellon and his PhD in Mathematical Sciences from Johns Hopkins. Since
1989, he has taught at Harvey Mudd College, where he is Professor of
Mathematics and past Chair. In 2000, he received the Haimo Award for
Distinguished Teaching by the Mathematical Association of America.
Currently, he serves as the MAA's Polya Lecturer from 2006 to 2008.
His research interests include combinatorics and number theory, with a
special fondness for Fibonacci numbers. Many of these ideas appear in
his book (co-authored with Jennifer Quinn), "Proofs That Really Count:
The Art of Combinatorial Proof", published by MAA. In 2006, that book
received the Beckenbach Book Prize by the MAA. Professors Benjamin
and Quinn are the editors of Math Horizons magazine, published by MAA.
Art is also a magician who performs his mixture of math and magic to
audiences all over the world, including the Magic Castle in
Hollywood. He has demonstrated and explained his calculating talents
in his book "Secrets of Mental Math" and on numerous television and
radio programs, including The Today Show, CNN, and National Public
Radio. He has been featured in Scientific American, Omni, Discover,
People, Esquire, New York Times, Los Angeles Times, and Reader's
Digest. In 2005, Reader's Digest called him "America's Best Math
St. Mary's College of Maryland
Invited Address: The Geometries of Escher
A recurrent theme in the intoxicating images of M.C. Escher is the division
of the plane into animal figures. Underlying each division is a tiling of
the plane by simple polygons. Escher's spirit of artistic adventure led him
to explore more exotic patterns, and we will follow his path into tilings of
the sphere and of the hyperbolic plane.
Susan Goldstine received her A.B. in Mathematics and French from Amherst
College in 1993 and her Ph.D. in Mathematics from Harvard University in
1998. When she is not doing research in number theory and algebraic
dynamics, she enjoys making tactile and visual mathematical models employing
such diverse media as yarn, fabric, thread, glass beads, paper, steel wire,
copper tubes, pinecones, and pottery, though not all at once. Some of this
work can be seen at
She is also an avid
cook, and while she usually pursues non-mathematical cookery, she hopes one
day to reproduce the interlocking Escher swan cookies she made for a lark as
an undergraduate. Her institutional home is St. Mary's College of Maryland,
where she strives to maintain her reputation for having the office with the
Elizabeth Theta Brown
James Madison University
Mid-Banquet Slideshow: Some Images of Mathematical Art
We present selected images from the field of mathematical visual art,
including art influenced by mathematics and mathematical notions instantiated
in an artistic way.
Elizabeth Brown came to James Madison University following a postdoctoral
appointment as John Wesley Young Research Instructor at Dartmouth College and
graduate work at Boston University. Her mathematical research is in set
theory. Her other academic interests include the teacher training of
mathematics graduate students for college and university careers, the
philosophy of mathematics and science, and mathematics in fine and performance
art. Before discovering the joys of mathematics, she studied epistemology in
the context of analytic philosophy for a first Master's. She is a 2002-3
Project NExT fellow. She has the dubious honor of being a winner of the 2007
JMU Mathematics and Statistics Department Pi Day contest (held on March 14 at
1:59), in which students donate money to a charitable cause in order to be able
to throw pies at the top faculty earners.
Advance Mills, Virginia
Exhibit: Organic Geometry
I have chosen to work with mathematical themes in my watercolor paintings as a
way of expressing the timeless beauty of the universe around us. That the universe can
have structure and order, and at the same time be evolving through chaos and entropy
inspires my imagination.
Judith Townsend’s artistic life began with original contemporary quilted wall hangings.
Feeling limited by the time involved in creating quilts by hand, she explored other mediums
and found watercolor especially suited to the ideas she wanted to express.
The paintings can be described as structured abstracts which are inspired by discoveries in science,
the elegance of pure mathematics, and the rhythms of nature. She often employs a grid which can be
perceived as an obstacle to clear vision or a window through which reality is revealed. In the grid
structure can be seen the watercolor paintings’ evolution from quilts.
Originally from New England, Judith has lived in Advance Mills, Virginia since 1984. She graduated
from Windham College in Putney, Vermont (where she studied mathematics with Robert Lewand), and
received her master’s in elementary education from Antioch New England. She has worked in the field
of alternative energy, taught in a three-room school in Marlboro, Vermont and served as executive
director of the Charlottesville-Albemarle (Virginia) Clean Community Commission.