Frank Farris, Santa Clara University
Title of Talk: Forbidden Symmetry-Relaxing
the Crystallographic Restriction
Abstract: If you look at enough swatches of wallpaper,
you will see centers of 2-fold, 3-fold, 4-fold, and 6-fold
rotation. Why not 5-fold centers? They cannot occur,
according to the Crystallographic Restriction, a fundamental
result about wallpaper patterns, which are defined to be
invariant under two linearly independent translations.
Even so, we offer convincing pictures that show wallpapers
with 5-fold symmetry. How can this be? The talk is intended
to be accessible to students who know something about level
curves in the plane and linear algebra.
Biographical Sketch: Frank Farris serves as
editor of Mathematics Magazine through 2005. He hopes
to continue its tradition of inspiring and challenging
teachers and students of mathematics at the undergraduate
level. Awards include a Trevor Evans Award for his article
"The Edge of the Universe" in Math Horizons and the
David E. Logothetti Teaching Award at Santa Clara University,
where he has taught since 1984.
David Holmes, The College of New Jersey
Title of Talk: Who was the Author?
Using Statistics to Investigate Authorship of Anonymous
Works of Literature
Abstract: This talk looks at the science of stylometry
- the statistical analysis of literary style. The evolution
of stylometric methods is covered, followed by some case
studies using modern computer-based techniques. The importance
of statisticians working with specialists in the application
area e.g. historians, classicists, is stressed throughout.
Biographical Sketch: Dr David Holmes is a
Professor of Statistics at The College of New Jersey. Prior
to this he was a Principal Lecturer in Statistics at the
University of the West of England, Bristol, where he founded
the Bristol Stylometry Research Unit. He has published widely
in the field of stylometry and has given many presentations
on both sides of the Atlantic. He is a former Secretary
of the Association for Literary and Linguistic Computing.
Joseph O'Rourke, Smith College
Title of Talk: Folding Polygons
to Polyhedra
Abstract: To *fold* a polygon means to glue its
perimeter to itself, so that there is no overlap, and no
gaps, and the resulting surface is homeomorphic to a sphere.
This talk will examine the surprisingly rich question of
which polygons can fold to which polyhedra, with special
(but not exclusive) concentration on convex polyhedra.
Although most polygons cannot be folded to any convex polyhedron,
every convex polygon folds to an infinite number of incongrent
convex polyhedra. To give a sense of the possibilities,
we have established that the familiar Latin cross polygon
can fold to a cube, and to exactly 22 other incongruent
convex polyhedra. We will describe the connection to a deep
theorem of Alexandrov, and introduce a variety of approachable
unsolved problems.
Workshop Title: Folding Polygons
to Polyhedra
Description: The corresponding
workshop will have participants cutting out polygons and folding
them, as well as exploring continuous analogs, the elegant "pita
forms" and "D-forms."
Biographical Sketch: After graduating from St.
Joseph's University (physics and mathematics), Joseph O'Rourke
studied computer science at the University of Pennsylvania,
from which he received the Ph.D. in 1980. He then joined
the faculty of Johns Hopkins University as an Assistant
Professor. He was promoted to Associate in 1985, and then
left in 1988 to found and chair the Computer Science Department
of Smith College, as the Olin Professor of Computer Science.
Currently he is again chair of the department.
