|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
- Thursday, October 23:
Colloquium at 4:00 p.m. in VWF 104.
October 25: Michigan Undergraduate Mathematics Conference
October 29: Problem of the Fortnight due by 3:00
October 30: Colloquium at 4:00 p.m. in VWF 104.
November 1: MATH Challenge from 9:30 a.m. to 12:30 p.m.
Professor Tanis will show how Maple can help you become an artist
|If you thought the
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
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
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
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!
is a game played according to certain simple rules with meaningless
marks on paper. David Hilbert (1862-1943)