OFF ON A TANGENT
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
October 22, 2003 Vol. 2, No. 4


Here's what is coming up in the next fortnight
Professor Tanis will show how Maple can help you become an artist 
 
If you thought the computer algebra system Maple could just help you solve a differential equation or evaluate an integral, you are wrong.  Professor Emeritus Elliot Tanis will show us, in tomorrow's colloquium, that Maple can be used to make art by using the commands translate, rotate, and reflect.  On  Thursday, October 23, at 4:00 p.m. in VWF 104, Professor Tanis will present  "Using Maple to Construct Repeating Patterns and Tessellations Inspired by M.C. Escher."  He will be using examples from Chinese lattice designs, M.C. Escher's tessellations, and other sources.  The way in which tessellations are classified will be illustrated and examples of some of the 17 plane symmetry groups will be shown.

Wings by Elliot Tanis


Next week's colloquium to be presented by a member of the GVSU faculty

Next week's colloquium will be presented by Paul Fishback of the mathematics department of Grand Valley State University.  Dr. Fishback talk is titled, "An Oxymoronic Derivative Definition" and will be presented Thursday, October 30 at 4:00 p.m. in VWF 104.  In this talk, he will show that there are other ways to define a derivative than what is taught in a traditional calculus course. 

In particular, in the winter of 1985, as part of an undergraduate research project, Daniel Kopel, a classmate of the speaker, formulated what he considered to be a new derivative definition. Dan called his new derivative the Least Squares Derivative, as it was based on the continuous analog of what statisticians refer to as the least squares regression line. Dan showed that his definition was an extension of the derivative in the sense that if the normal derivative exists at a point, then so does the least squares derivative. He also constructed an example of a least squares differentiable function that is not differentiable in the normal sense, thereby showing his definition was a proper extension of the derivative. The results of Dan’s findings were published in the American Mathematical Monthly in 1990. That Dan had to use the definite integral, a topic normally introduced in calculus after the derivative, to define his least squares derivative, motivates the title of this talk.


Mathematical Jeopardy! winners announced     

The answer is, "This is a sound a bear makes or is the name of the winning Mathematical Jeopardy! team."  What is Grrrrrr?  Congratulations to Jon Sedon, Nick Sumner, and Andrew Wells on Grrrrreat performance in Mathematical Jeopardy!  Second place was taken by The Harmonic Oscillators, a team of Calculus I students. Coming in third place was Kyle's Team.  Congratulations and thanks go to all who participated in this fun event.


Problem Solvers of the Fortnight

Congratulations to Mike Nelsen, Nick Sumner and Sara Tatge, all of whom correctly determined that only two colors are needed to color the map formed by a finite number of intersecting circles in the plane. The key to this problem is that each region is contained in either an even or an odd number of circles, and hence can be colored accordingly. The blue ribbon prize this fortnight is awarded to Nick Sumner for his elegant solution using a parity argument.


Colorful Web sites

The famous four-color theorem made an appearance in Math Jeopardy at last week's colloquium and lurked in the shadows of the Problem of the Fortnight. First conjectured by F. Guthrie in 1853, the problem of determining how many colors are needed to color any map was not settled until 1977 by Appel and Haken. To read more about the interesting history of the four-color problem, see http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/The_four_colour_theorem.html and for more about the ideas and concepts of the problem, check out http://en.wikipedia.org/wiki/Four_color_theorem and  http://mathworld.wolfram.com/Four-ColorTheorem.html.


The Problem of the Fortnight   

Halloween is coming, and the local Werewolves Club is having a joint meeting with the Goblins Group. At the beginning of the meeting, everyone shakes hands with each and every member of his or her own club. At the end of the meeting, everyone shakes hands with each and every member of the other club. It is found that the total number of handshakes that happened at the beginning of the meeting is the same as the number at the end of the meeting. Also, it is found that there are 11 more werewolves than goblins. How many members are in each club?

Write your solution (with proof!) on the back of your hand (or a piece of paper, or maybe a pumpkin), and bring it to Dr. Pearson's office by midnight on Halloween.


Visit the mathematics departments home page

The home page for the Hope's mathematics department can be found at http://www.math.hope.edu.  Here you can check out past issues of Off on a Tangent, look at the colloquium schedule, and find information about your degree, competitions, or summer research.  You can also find links to your favorite professor's web page.  Check it out!
 

Mathematics is a game played according to certain simple rules with meaningless marks on paper.  David Hilbert (1862-1943)