OFF ON A TANGENT
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
February 28, 2007
Vol. 5, No. 11
http://www.math.hope.edu/newsletter.html


Chaotic Colloquium this Thursday
What do the continental divide, the flap of a butterfly's wings and a straw on a camel's back have in common?  Why are tree branches, mountain ranges and your circulatory system "self-similar"?  How can simple mathematical formulas command computers to generate incredibly complex and intricate pictures?

Exploring the world of chaos and fractals, we will see how the study of mathematical dynamical systems leads to a better understanding of natural forms and processes.  (If you already have the universe figured out, don't bother coming to this colloquium!)

  Join us for Tea Time on Thursdays before colloquia

As part of our colloquium series this year, the mathematics department will host a "tea time" in the Reading Room (VWF 222) at 3:45 pm.  If tea isn't really your cup of tea, have no fear -- we'll provide some other beverages and snacks, too.  So please join us for a little food and fellowship before you go to the colloquia.  It'll be a great time to chat with the speaker, your professors and other students.

Bowlizza!

On Saturday, February 17, about 45 math students and faculty descended on the Holland Bowling Center for the math department's fourth annual bowlizza (= bowling + pizza) extravaganza.  After bowling a couple games, the crew returned to Van Zoeren for pizza and a game, from which we learned, among other things, that one of the bowlizzers had fallen off a roof twice, that another had not showered since Thursday (though he claims to shower "pretty regularly"), and that the name of another means "right-handed" in Hebrew. 

Kudos to the Stats 310 class, who had both the highest individual score (181) and the highest mean score (129.54).  They also amassed the most strikes (30) of any class.  The Multi 1 class took the prize for the highest standard deviation in scores (41.73), and the 300-level classes bowled the most consistently with a standard deviation of 17.89.  The bowling results are posted on the bulletin board in the main hallway on the second floor of Van der Werf. Thanks to all who participated.  It was a fun and lively start to the weekend!    

Hope Awarded 5-year REU Grant

The Hope College Mathematics department is pleased to announce that it has received a five-year REU (Research Experiences for Undergraduates) grant from the National Science Foundation.  The grant will provide students with funding for eight weeks of summer mathematics research with Hope mathematics faculty and some additional travel allowance for students to present their work at mathematics conferences.  Application materials for the 2008 Hope mathematics REU program will be available online next academic year.  It's never too early to start planning, and so we encourage math majors to talk with their advisers and keep in mind the possibility of doing mathematics research next summer.


Lower Michigan Mathematics Competition
The 31st annual Lower Michigan Mathematics Competition (LMMC) will be held Saturday, March 31, 2007 at Calvin College.  The competition consists of a 10-problem exam taken by teams of 2 or 3 undergraduates and will last about three hours.  Lunch will be provided for participants.  The Hope Mathematics Department will provide transportation to and from the competition.  The schedule of the day's activities for the 2007 LMMC is:

8:45am - 9:15am Check-in and refreshments in the Atrium of DeVries Hall
9:30am -12:30pm Competition
12:30pm -1:30pm Lunch
1:30pm - 2:30pm Solution session

The highest scoring team earns the right to take home the coveted Klein bottle trophy, shown above in the first floor VWF display case, where we hope it will reside next year!

To register for the 2007 LMMC, sign up on one of the registration sheets that will be circulated in classes over the next few weeks, or add your name to the registration sheet on Dr. Cinzori's door by noon on Thursday, March 15.


Graduate School Panel
Are you thinking about going to graduate school?

There will be a panel discussion on graduate school on Thursday, March 1 between 11:00 and 11:50 a.m. in the Herrick Room (DeWitt).  Panelists include Tammy Van Dyken (History), Melissa Villarreal (Social Work), Todd Wiebe (Van Wylen Library) and Melissa Mulder (Spanish).  They will speak on topics such as how to pick graduate programs, the application process and how to finance graduate education. They will also answer students’ questions.


This Day in Mathematics History . . .

On February 28, 1735, Alexandre-Théophile Vandermonde was born in Paris.  As a child, Vandermonde had little interest in mathematics; he was passionate about music, loved playing the violin and intended to pursue a career in music -- which he did until age 35!  His interest in mathematics was sparked late in life by his friend Fontaine des Bertins, whose enthusiasm for mathematics was contagious.  Not surprisingly, Vandermonde's first mathematical forays explored a mathematical basis for music, but he is best known for his work with determinants, called Vandermonde determinants in his honor.  The mathematician Thomas Muir said that Vandermonde is the "only one fit to be viewed as the founder of the theory of determinants" because he was the first to view them as functions rather than simply as a tool used to solve systems of linear equations.  Please visit http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Vandermonde.html or click on the link above to read more about Vandermonde. 


Problem of the Fortnight 

Let C be a circle of radius 1.  Pick two points on C at random (using a uniform distribution on the circle so that each point on the circle has an equal probability of being chosen). 

What is the expected value of the length of the chord connecting the two points?

Write your solution on a circular sheet of paper and drop it in the Problem of the Fortnight slot outside Dr. Pearson's office (VWF 212) by 3 p.m. on Friday, March 9.  As always, please be sure to include you name, the name(s) of your math professor(s), and the math class(es) you are taking -- e.g. David B. David, Circular Logic, Professor Roundabout -- on your solution.


Problem Solvers of the Fortnight 

The area enclosed by a polar equation curve r = f(θ) is given by A = 1/2 0∫ 2π r2 dθ .  If we integrate r = 1 - 2 sin θ  from 0 to 2π, we will count the area of the inner loop twice.  (Do you see why this is true?)  Therefore, since the inner loop is traced out as θ goes from  π/6 to 5π/6, the area between the inner and outer loops is
A = 1/2 0∫ 2π(1 - 2 sin θ)2 dθ - 2 [1/2 π/6 ∫ 5π/6 (1 - 2 sin θ)2 dθ ]
= 1/2 0∫ 2π(1 - 2 sin θ)2 dθ - π/6 ∫ 5π/6 (1 - 2 sin θ)2 dθ. 
Using techniques of integration, we evaluate this integral to find A =π + 3√3.

Congratulations to Jeff Meyers and Jeff Shriner for wending their heartfelt way around this lovely problem.


50-Cent Book Sale!

The 50-cent math book sale continues!
Stop by VWF 222 to look at the available books,
and when you find one,
drop off 50 cents in the math department office. 
What a deal!


Algebra and money are essentially levelers; the first intellectually, the second effectively.
~ Simone Weil (1909 - 1943)