Pi Mu Epsilon - Mathematical Association of America

Thursday Pi Mu Epsilon Session #1 August 2, 2012
PME Session #1
Room: Meeting Room O
2:00P.M. – 3:55P.M.
2:00–2:15
Anagrams, Markov’s and Knots
Liliana Alvarez
Austin Peay State University
Our research objective is to observe the interplay of words created from scrambled letters in relation
to Markov chains. Thereafter, we will study the words with regards to different types of knots.
We applied stochastic modeling to anagrams that formed Markov chains. We used graph theory as
an instrument to see the linkage between the world of literature and knot theory.
2:20–2:35
Vertex Polygons
Candice Nielsen
Elmhurst College
We identify necessary conditions for equal-area hexagons to have vertex quadrilaterals with equal
area, discover a method for creating a hexagon whose vertex quadrilaterals have equal area without
being equal-area, and generalize to construct any polygon with an even number of sides to have
certain vertex polygons with equal area.
2:40–2:55
4-move Reducibility of Cables of (2p + 1, 2) Torus Knots
Andrew Tew
University of Nebraska at Omaha
In 1979, Y. Nakanishi conjectured that the 4-move operation is an un-knotting move. This conjecture
is assumed to be false, even though no counterexample has been found and every knot with
12 or fewer crossings has been verified as being 4-move reducible to the unknot. It was believed
for sometime that the 2-cable of the trefoil knot was a potential counter-example to the 4-move
conjecture. However, in his paper “A Note on 4-Equivalence”, Nikolaos A. Askitas presented a
sequence of 4-move (along with ambient isotopies) that reduced the 2-cable to the unknot. Askitas
claims that an inductive proof exists that all 2-cables of (2p+1, 2) torus knots are 4-move reducible
to the unknot. This project seeks to explore the inductive argument.
3:00–3:15
The Complement of Fermat Curves in the Plane
Ariel Setniker
Western Oregon University
A plane algebraic curve is a curve defined implicitly by a relation of the form f(x, y) = 0, where
f(x, y) is a polynomial in x and y. A curve is said to be rational if it can be parametrized by
rational functions x(t), y(t). In this talk we will discuss necessary conditions for a rational curve
to be defined on the complement of high degree algebraic Fermat curves.
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