November 7, 2000 Volume 29, No.9

St. Olaf Mathematics Department 

Math  Mess

November 7, 2000 Volume 29, No.9

New Point System!!
The Mathematics Department is proud to announce a new point system associated with the colloquium series.  Each week the Editorial staff of the Math Mess will pour over reams of information and data supplied by the speaker about the talk, then unanimously agree upon an appropriate point level.  The student who accumulates the most points by the end of the semester will win a variety of items.  First and foremost, there is the personal satisfaction of having attended a bunch of mathematics colloquia.  Other than that, there might be a math department t-shirt involved, maybe $1000 or so, etc. Start earning points now by attending this week’s talk by St. Olaf’s own Bob Breid.

This Week’s Colloquium
Every juggling pattern is a unique combination of properties: timing of throws and catches, heights of throws, arm motions, body movement, etc. How can one express a juggling pattern in writing?  If every tiny detail were recorded, pages could be filled on simple patterns.  Thus, some details must be omitted.  This presentation will concentrate on what is termed the “vanilla siteswap,” where the juggler’s hands are more or less stationary and the throws alternate between right- and left-handed throws. Some of the topics to be explored include: time-space diagrams, vanilla siteswaps, orbits, ground state patterns, landing patterns, and excited-state patterns.

This Week’s Speaker
Bob Breid grew up in Lakeville, MN and attended college at North Dakota State University in Fargo, ND.  He pursued a double major in Computer Science and Mathematics, and graduated in the fall of 1998.  Now a UNIX systems administrator for St. Olaf College, Bob oversees the operation of a dozen servers and provides support for about 60 lab, classroom, and office computers. In his spare time, he enjoys programming, bowling, golfing, reading, and yes, juggling.

Math Contest
The annual Carlson Calculus Contest will be held on Nov 14 and 15 this year.  The contest is open to any student who has not enrolled in Math 220 or a higher-level math course.  Students will pick up an exam sometime between 4 and 7 PM and work in teams of three for 90 minutes (not two hours).  The exam will consist of 8 or 10 problems which calculus students may find amusing.  So, get a team together for the contest to be eligible for a total of over $200 in cash prizes. You may preregister by e-mail at corzatt@stolaf.edu.

Math Tutors
Volunteer math tutors are needed to work with elementary and secondary school students in Northfield, Monday evenings, Tuesdays after school, and possibly other times. Please contact Kay Smith in OMH 209 or e-mail smithk if you are interested in volunteering.

T-Shirt Designs
The MAA chapter will once again be offering Mathematics Department t-shirts for sale and is seeking design suggestions. Anyone with a design (front or back of shirt) should submit it to Ted Vessey, OMH101. The winner(s) will get due recognition and two free shirts.

Actuarial Fair
The University of Minnesota is hosting an Actuarial Career Fair on Thursday, November 16 from 4-6pm.  It will be in the lower level dining room in the Carlson building.  About 17 companies will be there.

Politics
Press time for the Math Mess is Monday, so at this point it is unknown who the next president of the United States will be.  The staff of the Math Mess is going out on a limb to congratulate either Al Gore or George W. Bush on his win.

Last Week’s Solutions
Problem: Let a(1), a(2), … a(44) be 44 integers with 0<a(1)<a(2)<a(3)….<a(44)<126. Prove that at least one of the 43 differences d(i)=a(i+1)-a(i) occurs at least 10 times.

Solution: To minimize the sums of the differences, start with nine 1s, then nine 2s, nine 3s, nine 4s, and seven 5s.  This adds up to 125, and the first term is greater than zero, so the last term would have to be at least 126, which is too high.  Therefore, there must be at least 10 of one of those differences in order to keep the terms within the range of 0 to 126.

*Solved by Michael Zahniser, Bob Hanson, Brett Werner, Bob Breid, Robert Hilliad, Paul Tlucek and Jonathon Kuipers.

Problem of the Week
Again we owe thanks to David Molnar for suggesting this one: Find the exact value of the power series (1/4)+(1/8)+(2/16)+(3/32)+(5/64) +(8/128)…, where the nth term is the nth Fibonacci Number divided by 2(n+1) .

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

Correction:  George Polya was Hungarian, not Greek, as was reported last week.

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