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Mathematical Sciences

Sammy Black, Linfield College

Date: 3:30pm PDT March 20, 2012 Location: JR Howard Hall, Room 114

JR Howard Hall, Room 114

Mathematical Sciences Colloquium:

Untangling ropes using the Euclidean Algorithm

How tangled can two ropes be?  How can we tell if pulling on a loose end will tighten a knot or cause it to come undone?  Given a tangled mess of ropes, how do we twist and turn it to untie it?  These sorts of questions have intrigued mathematicians for over a century.  Surprisingly, in certain cases, the problem of tangles can be translated into the arithmetic of rational numbers.  The crucial connection, first observed by John Conway, involves continued fractions and draws on an observation recorded by Euclid more than two thousand years ago.

In this talk, I will tell you the story of Rational Tangles and their connection to the Euclidean Algorithm for finding greatest common divisors.  Then, we’ll put this theory to the test with the help of some volunteers.  This talk should be accessible to any college student.