October17, 2000 Volume 29, No.6

St. Olaf Mathematics Department 

Math  Mess

October17, 2000 Volume 29, No.6

This Week’s Colloquium
You go to the closet to pull out that extension cord that has been buried under years of memories.  It is a big tangled mess that takes you ten minutes to untangle. You are the victim of random knotting.
Some knots are easier to tie and, thus, more likely to occur in your extension cord.  This is one of many ways to measure the complexity of a knot.  Another strategy is to find the position of a certain knot that is optimal in some regard (e.g. it takes the fewest number of “sticks” or the least amount of rope to tie).  We will explore some measures of complexity, the relationships between these measures, and an application of optimal knots to molecular biology.

This Week’s Speaker
Eric Rawdon graduated from St. Olaf College (Um Ya Ya) in 1992 with a major in math and concentrations in African Diaspora and American Racial and Multicultural Studies. He received his Ph.D. from the University of Iowa in 1997 in Physical Knot Theory. Eric has been in a tenure-track position at Chatham College, an all-women’s liberal arts college in Pittsburgh, PA, for the last 3+ years. He enjoys playing golf, brewing beer, jogging, and traveling.

A Short Biography
Alan Turing was a mathematician who was a pioneer in the fields of logic, computer science and artificial intelligence.  Born in London in 1912, Turing earned his Ph.D. from Princeton University in 1938.  During his time at Princeton, he developed what has come to be known as the “Turing Machine.”
Turing was concerned with the question of determining if a theorem was true or not.  He reduced mathematical operations to their fundamental constituents, which were then fed into a “machine” (which he imagined to be an infinitely long tape).  While his machines successfully performed the mathematical operations, Turing was unable to prove that a general computation would ever stop.  He concluded that it is not possible to determine if a theorem is provable without actually finding the proof.  (Ed. Note: This is bad news for ERA students, but gives professional mathematicians a reason to live!)
What began as an experiment in purely abstract thinking turned out to be a precursor to today’s modern computers.  Indeed, Turing worked for the British government during WWII on machines that helped decipher German codes produced by the Enigma.
Turing was at the University of Manchester still doing research on computers when he committed suicide in 1954. It is widely believed that his suicide was a result of the depression he went through after being convicted of sodomy (being gay was a crime in Britain at the time) and sentenced to estrogen treatment. A tragic ending to a passionate thinker whose work is widely known.

Informational Meetings
*Students who are interested in grad school in statistics or biostatistics are encouraged to attend an Open House at the U of M on October 20th. If you are interested in attending please contact Sally Olander at 612-625-9185 or sally@biostat.umn.edu. More information can be found at www.biostat.umn.edu.

*The student chapter of the MAA will meet to organize and set plans for fall activities. All majors and others with an interest in mathematics are encouraged to attend (FREE root beer floats!). The meeting will be held in SC 130 at 7:30pm Tuesday, October 17th.

Last Week’s Solutions
Problem: A T-tetramino is a set of 4 unit cubes arranged in the shape of a capital letter T. Prove that if T-tetraminos cover the area of an m by n rectangle without overlapping then the product mn is a multiple of 8.

Solution by Michael Zahniser ’04 and Mark Krusemeyer: Clearly mn is a multiple of 4 since each tile has area 4. Color the squares of the m by n board black and white in a checkerboard pattern. Each tile covers three white and one black squares or three black and one white. Since the numbers of white and black squares are equal in number, when the board has one even dimension, there must be an even number of tiles. Hence mn is divisible by 8.

Problem of the Week
Suppose we wish to know which windows in a 36-story building are safe to drop eggs from, and which will cause the eggs to break on landing.
We make a few assumptions: 1) An egg that survives a fall can be used again. 2) A broken egg must be discarded. 3) The effect of a fall is the same for all eggs. 4) If an egg survives a fall, then it would survive a shorter fall. 5) If an egg breaks when dropped, then it would break if dropped from a higher window. 6) It is not ruled out that the first floor windows break eggs, nor is it ruled out that the 36th-floor windows do not cause an egg to break.
If two eggs are available, what is the least number of droppings required that is guaranteed to determine in all cases, the lowest floor that causes eggs to break?

**Please submit all solutions to Cliff Corzatt (corzatt@stolaf.edu) by noon on Friday.

To subscribe to the Math Mess, please contact the MM czar at brakke@stolaf.edu.

Editor-in-Chief: Jill Dietz
Associate Editor: Jennifer Beilfuss
Problems Editor: Cliff Corzatt
MM Czar:   Donna Brakke
mathmess@stolaf.edu