OFF ON A TANGENT
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
September 21, 2005 Vol. 4, No. 2
http://www.math.hope.edu/newsletter.html

Hope Floats Kegger deemed a success

As they say, a good time was had by all at our first get-together of the year for the mathematics students.  About 60 students and faculty attended the informal event to enjoy root beer floats, meeting other mathematics students, and root beer trivia.  The following pictures show much of the group that was in attendance and Elvis doing his part to help clean up afterward.


Colloquia Past and Future

Dr. Robert Megginson

Professor Robert E. Megginson, an Associate Dean and Professor of Mathematics at the University of Michigan, gave the first colloquium of the year last week Thursday.  About 50 students and faculty attended his talk that was titled “Native American Mathematics.”  He looked into the Mayan calendar system (which was quite complex) and showed how an understanding of modular arithmetic is needed to fully understand and work with this system.  It was all very interesting.

Drs. Elvis Bogart Wales and Tim Pennings

For tomorrow's colloquium, Elvis will be in the building as Professor Tim Pennings and his his canine companion will present their talk, "Do Dogs Know Calculus?" 

A standard modeling problem in calculus is to find the quickest path from a point on shore to a point in a lake where the running speed is greater than the swimming speed.  Elvis, Tim's Welsh Corgi, has never had a calculus course, but when he plays "fetch" on the shore of Lake Michigan, he appears to choose paths close to the optimal ones.  In this talk, it will be revealed what was found experimentally when Elvis was tested.  (You might want to stay after the talk to see Tim give Elvis instructions telepathically!)

Dr. Thomas Q. Sibley Next week's colloquium will feature Tom Sibley from St. John's University in Collegeville, Minnesota.  The title of his talk is "End Base Discrimination Now!" 

Some fractions get treated more "nicely" in base ten than others---just compare the decimal representations of 1/7 and 1/8. This talk expands the idea of a base in some playful ways. Along the way he will present a base that doesn't "discriminate" among fractions---every fraction has a finite "decimal" representation.


Statistics Career Day next month at GVSU

On Friday, October 14 the Southwest Michigan Chapter of the American Statistical Association (ASA) and the Grand Valley State University Department of Statistics will present a Statistics Career Day on their Allendale Campus.  Exhibits on employment in statistics from governmental agencies and private industry will be available as well as those from graduate schools.  There will also be a number of talks given about employment as well as a keynote address from ASA president Fritz J. Scheuren.

This event is free and the department will provide transportation and pay for lunch.  If you plan to use transportation provided by the math department, you should plan on leaving at 9:30 a.m. and returning to campus at 4:30 p.m.  For more information about this event you may contact either Prof. Bekmetjev (bekmetjev@hope.edu) or Prof. Tintle (tintle@hope.edu).  (Information can also be found at Statistics Career Day link in the preceding paragraph.)


The MATH Challenge is coming soon

The 2005 Michigan Autumn Take Home Challenge (or MATH Challenge) will take place on the morning of Saturday, October 29 this year.  Teams of two or three students take a three-hour exam consisting of ten interesting problems dealing with topics and concepts found in the undergraduate mathematics curriculum.  Each team takes the exam at their home campus under the supervision of a faculty advisor.  Hence there is no need to travel off to distance lands with exotic names like Kalamazoo, Sault Ste. Marie, or Flushing. 

Each year 20-30 teams compete in this competition with teams from Hope regularly placing in the top three.  (A team from Hope has won this event twice in its 11-year history.)  

For more information about this competition visit http://www.mcs.alma.edu/mathchallenge/.  If you are interested in competing, you need to sign up with Prof. Aaron Cinzori on or before October 12.


Math in the News: A new form of trigonometry

If you have trouble determining the difference between sine and cosine, a new form of trigonometry may just be for you.  Dr Norman Wildberger from the University of New South Wales has developed what he calls rational trigonometry.  It replaces sines, cosines, and tangents with arithmetic and replaces angles and distance with spread and quadrance.  He writes about this in his new book Divine Proportions: Rational Trigonometry to Universal Geometry.

For more information about rational trigonometry, you can read the article titled, "New trigonometry is a sign of the times" at http://physorg.com/news6555.html.  Thanks go out to Karl Buter for informing us of this new trigonometry.


Hope math prof wins Mt. Baldhead Challenge

Renea Walkotten, who is an instructor in the mathematics department, was the first woman to cross the finish line in last Saturday's Mt. Baldhead Challenge 15K race.  She finished the race, that included a climb up a 282-step stairway to the top of Mt. Baldhead, with a time of 1:03:20.  Prof. Walkotten is no stranger to winning races.  She was a multiple All-American runner in college (we won't mention where) and was the individual cross-country national champion in division III in 1993.

The Hope mathematics department has other connections to the Mt. Baldhead Challenge.  Professor Emeritus Rick Vandervelde holds the record for the 5K race in the 60 to 69 year-old category.   Hope senior and mathematics major, Ryan Weaver, holds the record in the 5K race in the 0 to 19 year-old category (as well as the course record).  Hope grad (and math major) Lee Kiesel '03 holds the record in the 20 to 29 year-old category.  Vandervelde, Weaver, and Kiesel all set these records in 2002.


Hope professors recently get text published

Professors Janet Andersen and Todd Swanson are co-authors of Understanding Our Quantitative World, which was published by the Mathematical Association of America this past summer.  The text was specifically written for the GEMS 100 course here at Hope, but can be used for other general education mathematics courses or quantitative literacy courses.

The emphasis in the text, is on helping students learn to use mathematics to interpret the world they encounter daily. Attention is paid in particular to interpreting graphs, simple functions, and statistical information.  This is done through real-life examples for such things as the stock market, the cost of Internet services, electric bills, and car loans.

Andersen and Swanson have been collaborating on developing courses and related texts for more than a decade.  They have previously published two other books along with Robert Keeley, an associate professor of education at Calvin College.


Let's play Mathematical Jeopardy!     

The original streaker, he is famous for is running naked through the streets of Syracuse yelling Eureka! Eureka!  It is a polyhedron with 20 faces.  It is the trigonometric term that also means a sun-burned man.  If you know the questions that go with these answers, then we have a colloquium for you.  The mathematics department will conduct a Mathematical Jeopardy competition on Thursday, October 20.  While this is still about a month away, it is not too early to think about forming teams.  All interested students are encouraged to participate.  More details about this event will be in the next newsletter.

The questions for the answers given at the beginning of this article are, of course, Who is Archimedes? What is an icosahedron? and What is a tangent?


Problem of the Fortnight

While we're still uncertain whether the chicken or the egg came first, we are certain that this fortnight's problem is one to crow about!  Sit on it for a while and see if you can hatch a solution!

Suppose you wish to know which windows in a 36-story building are safe to drop eggs from and which will cause the eggs to break.  We make a few assumptions:

* An egg that survives a fall can be used again.
* A broken egg must be discarded.
* The effect of a fall is the same for all eggs.
* If an egg breaks when dropped, then it would break if dropped from a higher window.
* If an egg survives a fall, then it would survive a shorter fall.
* It is not ruled out that the first floor windows break eggs nor that the 36th floor windows do not cause an egg to break.

If only one egg is available, then the experiment can be carried out in only one way: Drop the egg from the first floor, and if it survives the fall, drop it from the second floor; continue going up a floor at a time until the egg breaks.  In the worst case, this method would require 36 droppings.

Suppose that two eggs are available.  What is the least number of egg drops in the worst case scenario you need to make in order to determine with certainty which floor is the last safe floor from which you can drop an egg?  

Write your solution on an egg carton and drop it (sorry -- couldn't resist) by Dr. Pearson's office (VWF 212) by 3:00 p.m. on Friday, September 30.


Problem Solvers of the Fortnight

Congratulations to Jeff Ambrose, Rachel Bakken, Benjamin Crumpler, James Daly, Erica Dickinson, Abbey Finn, Maya Holtrop, Bryan Johnson, Katie Johnson, Lisa Kallemeyn, Kristine Krcmar, Rachelle Kreuze, Ellie Krohmer, Travis Love, Heather McGovern, Keith Mulder, Karen Nordell, Rob Schaftenaar, Karena Schroeder, Tiffany Slokum and Evan Van Heukelom, all of whom correctly determined that the seating rearrangement problem was impossible. 

The solution to the problem essentially involves a parity argument, and perhaps the best way to state it is as follows: Think of the 25 seats in the class as sitting on a chessboard with alternating red and black squares.  Then any move that is allowed will involve changing color.  But if there are originally 13 red squares, say, then the 13 people sitting in those chairs must each move to a black square, of which there are only 12, and hence the proposed rearrangement is impossible.


M*A*T*H in the media

"NUM3ERS," the hit CBS television drama about a mathematician who helps his FBI agent brother, enters its second season on the air with the season premiere this Friday, September 23.  Interestingly, the mathematics featured in each episode is based on real FBI cases.  In conjunction with CBS, Texas Instruments has launched a new web site called "We all use math everyday" (http://www.cbs.com/primetime/numb3rs/ti/) that offers interactive mathematics activities based on the mathematics of each episode.

"Proof," a play by David Auburn that won both the Tony Award and the Pulitzer Prize for drama in 2001, has recently been made into a movie starring Jake Gyllenhall, Gwyneth Paltrow, Anthony Hopkins and Hope Davis.  The movie focuses on the struggles of the daughter of a brilliant but mentally disturbed mathematician.  Directed by John Madden (not the football commentator for Monday Night Football), "Proof" opened in select theaters last Friday, September 16.  It opens to wide release on September 30.  To visit the official web site for the movie go to http://www.miramax.com/proof/ .


Got a Math Question?

Ask Elvis ...

... email him at elvis@hope.edu

Dear Friends,

I often find newspaper headlines amusing. It seems that newspaper editors share my enjoyment of puns.  For example, as I was reading the Grand Rapids Press last week Wednesday (yes I find newspapers to be more than a puppy training tool), I noticed the headline on the front page said, "Will cuts spank Young Fives?"  I thought that was an interesting verb choice.  As I read on, I saw that the headline on the top of page B1 read, "Surgical center takes off gloves."  Nice.  The entertainment section also added one with, "Fox sitcom full of flaw and disorder."  The sports editor didn't let me down either, with "Temple schedule nothing to hoot about."  (Did you know that Temple's sports teams are known as the owls?)

All this came from one day in one paper.  That got me thinking, it seems the editors here at Off on a Tangent could spice up their headlines by making them a little more pun-iful.  I mentioned this idea to them and they said they would work on it.  We'll see what happens

The picture of sleeping above is my way of telling you that I didn't receive any questions this past fortnight.  My mail box was just full of spam.  Don't hesitate to write as I look forward to answering your questions.  Just drop me a line at elvis@hope.edu.



P.S.  I hope to see many of you at the colloquium tomorrow!












Headlines that weren't

Well Elvis, we took your advice and have been thinking about some possible headlines.  Here is the start of our list. Perhaps next fortnight we will start to work this idea into actual headlines.

The theory of groups is a branch of mathematics in which one does something to something and then compares the results with the result of doing the same thing to something else, or something else to the same thing.  

James Newman  1907-1966