OFF ON A TANGENT

A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics

March 31, 2004

Vol. 2, No. 12

Ken Vandenoever is shown here working hard on a project during a colloquium last month.  As the weather is getting warmer we can now leave our monster hats at home when we go to class.  While this warmer weather makes it tempting to put our studies aside and go out and throw the frisbee, it is important to give your studies your best effort right up until the end.  Don't let your hard work from the beginning of the semester go to waste at the end.

Putnam Results

The William Lowell Putnam Mathematical Competition, administered by the Mathematical Association of America, is the most prestigious mathematical competition for undergraduates in the nation.  Last December four Hope College students competed in this contest.  The results of this competition have just been published. Peter Van Wylen's score placed him in the top 11% of all students taking the test and Michael Rininger's score placed him in the top 60%. Congratulations to both of them.


Colloquium on graph pebbling slated for tomorrow

In tomorrow's colloquium, Professor Airat Bekmetjev will give us an insight into one of his areas of research; graph pebbling.  The talk is schedule for Thursday, April 1 at 4:00 p.m. in VZN 297.  Pebbling is a game that can be played on any connected graph.  Some number of pebbles are first placed on each vertex.  The player can move pebbles along the edges, but there is a toll for any move.  For every pebble moved across an edge the player loses one pebble. A configuration of pebbles is called solvable if the player is able to place a pebble on any vertex.  Two of the interesting questions that arise from this game are, "How many pebbles are enough to guarantee that any configuration is solvable?"  and "What are the optimal ways to move pebbles?"  In this colloquium Dr. Bekmetjev will answer these questions and discuss the existence of the threshold phenomenon in pebbling.


Many Hope students will be conducting mathematics research this summer

Hope College is always a buzz with activity during the summer and this summer will be no exception.  A number of students will be doing research in the mathematics department.  Hope students Kyle Williams, Ryan Weaver, and Ryan Ter Louw (along with Jocelyn Sikora from Carnegie Mellon) will be working on modeling projects with Prof. Pennings.  Hope student Daniela Banu (along with Erin Wicker from Alma, David Levitt from Carnegie Mellon, and Andrew Craker from Notre Dame) will be working on applied linear algebra projects with Prof. Cinzori.  Hope students, Mike Cortez, Jennica Skoug, Mike Nelson, Brandon Alleman, and Sam Lien will be working with Prof. Anderseon on mathematical biology projects.  In addition to these students working at Hope, Andrew Wells will be doing mathematics research this summer at SUNY Potsdam.


Math 208 students work as problem solving mentors

The students in Math 208: Problem Solving for Elementary Teachers are mentors for the Math Forum pre-algebra problem of the week website.  You can see their smiling faces and a link to the current problem of the week at http://www.mathforum.org/prealgpow/mentors/bio.ehtml?mentor_group=16.


Information about graduate school and the GRE available

There will be an information session on the Graduate Record Examination on Thursday, April 1 between 7:00 and 8:00 p.m. in Science Center 1000. This session will be led by Professor Charles Behensky of the Department of Psychology.  He will focus on the mechanics of the GRE and what students might do to prepare for the exam.

There will also be a panel discussion on graduate school, which will take place on Tuesday, April 6 between 11:00 and 11: 50 a.m. in the Otte Room of Phelps Hall. Panelists include Gloria Tseng (History), Karima Jeffrey (English), Isolde Anderson (Communication) and Chuck Behensky (Psychology). They will speak on topics such as how to pick graduate programs, how to finance graduate education and the application process. They will then answer students questions.


Problem Solvers of the Fortnight: Chompers!

Congratulations to Mike Nelsen and Dr. Pearson's mom for correctly solving the Chomp puzzle from the last issue!  Both outlined strategies for successfully avoiding the "chocolate-covered broccoli" square in the lower left-hand corner of various grids.  (Dr. Pearson thinks it's ironic that his mom, the person who fed him broccoli for all those years growing up, should reveal her broccoli avoidance tactics only now.)  For having his name drawn at random from among the correct solutions we received, Mike will receive a coupon to chomp on a pizza from Pizza Hut. . . .  And Dr. Pearson promises to take his mom out for a cup of coffee and a stalk of chocolate-covered broccoli sometime.


Problem of the Fortnight

Consider two concentric circles with radii 1 and x, where x < 1.  In the annulus determined by these two circles, 6 circles are constructed in the following way: each circle is tangent to the inner circle, the outer circle and the two adjacent circles.  Determine the value of x for which this is possible.  Write your solution on an annular piece of paper and drop it by Dr. Pearson's office by 3:00 p.m. on Thursday, April 8.

Mathography

Our featured mathematicians this fortnight are Rene Descartes (b. March 31, 1596) and Sophie Germain (b. April 1, 1776 -- no fooling!).  A contemporary of Galileo and Pascal, Descartes is perhaps most famous for his application of algebra to geometry, which is now sometimes called Cartesian geometry in his honor.  One of the more famous curves in Cartesian geometry is the folium of Descartes, and in this issue we highlight this interesting curve (see below).  To read more about Descartes, see http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Descartes.html. 

Sophie Germain is probably remembered most for her work on Fermat's last theorem (which was not proved until 1994 by Andrew Wiles), though she had many interesting mathematical correspondeces in her lifetime, notably with Gauss and Lagrange.  The middle daughter of a prosperous silk merchant, Sophie was a determined scholar even in her youth, reading Newton and Euler in bed at night---despite the fact that her parents had taken away her lamp in an attempt to force her away from her books!  Her determination persisted to the end; striken with breast cancer in 1829, she continued to publish interesting and insightful mathematical papers until her death in 1831.  To find out the facts that are germane to Germain, see http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Germain.html.


Graphography

In this issue we feature the famous folium of Descartes, the Cartesian equation of which is x3 + y3 = 3xy.  Though something of a misnomer, the name "folium" was given to this curve by Descartes based on his mistaken belief that the leaf shape in the first quadrant, which Descartes had correctly determined, repeated itself in the other four quadrants, like four petals of a flower.  (Yes, even great mathematicians make mistakes!)  See http://www-gap.dcs.st-and.ac.uk/~history/Curves/Foliumd.html for more on this famous curve, as well as an interactive JAVA applet that allows you to play with this curve and some of its associated curves.

"The whole problem with the world is that fools and fanatics are so certain of themselves, but wiser people so full of doubts."
-- Bertrand Russel (1872-1970)