OFF ON A TANGENT
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
October 19, 2005 Vol. 4, No. 4
http://www.math.hope.edu/newsletter.html


Tomorrow's colloquium is Mathematical Jeopardy!     
Tomorrow's the day for playing Mathematical Jeopardy!  We have about 7 teams signed up with names like Complex, Team Goldbond, and Ken Jennings.  There are also rumors around that there is a team of old math majors that might be joining the game. If you are not among those that have signed up to play and still wish to, you may sign up until 4:00 p.m. today (Wednesday).  You can do so as a team or individually.  To sign up to be a contestant, sign up on Professor Stephenson’s door (VWF 210) or by email him at stephenson@hope.edu.

Next week's colloquium will feature the 100-Digit Challenge
In a colloquium a couple of weeks ago we learned about the Poincaré Conjecture.  This is one of the seven Millennium Prize Problems and  $1,000,000 prize goes to anyone that can solve one of these problems.  Here at Hope, you will find that our professors are also lured by "big" bucks to solve problems. 

This week's colloquium is titled "What I (Re)-Learned From the 100-Digit Challenge."  It will be presented by Professor Aaron Cinzori on Thursday, October 27 at 4:00 p.m. in VWF 104.  In this colloquium, Prof. Cinzori will explain how he along with a team of mathematics and engineering faculty here at Hope could not resist a deal to earn $100 for solving 10 math problems in a competition with teams from all over the world in the 100-Dollar 100-Digit Challenge.  Most of the problems are stated simply and  involve integration, matrix calculations, minimization, probability, or geometry.  He will look at a few of the problems and their solutions as well as discuss problem solving in  general.  He will also give reasons why taking Numerical Analysis (offered next semester) can be useful.


It is never too early to start thinking about summer research

Imagine going to college and having no exams!  Or getting paid for going to college instead of paying to go!  Sound too good to be true?  Not only is it true, but over 100 science students take part in it every summer at Hope College, including about 10 in mathematics.  Many of them are your classmates.  They have done things which students normally do not experience until well into their graduate careers.  Some have presented their research papers at professional meetings, others have their names on research papers which have been published, and others have submitted their own individual paper for publication.

One research program that Hope continues to have is the National Science Foundation Research Experience for Undergraduates (NSF-REU).  Under this program, professors Mark Pearson, Airat Bekmetjev, Aaron Cinzori, and Tim Pennings will be working with students this summer.  Although students apply from all over the country for this program, Hope students are given special consideration.  This year's projects will come from the following mathematical areas: Algebra and Topology, Combinatorics and Probabilistic Models, Experimental Mathematics, and Modeling. 

If you are interested, see the web site at http://www.math.hope.edu/reu.html for more details.  If you are interested in doing summer research, but not at Hope, check out the other REU sites around the country.  A list of these can be found at http://www.maa.org/students/reustuff/pages/REU.html.  The deadline for applying to  an REU is usually during the winter, but it is never too early to start making plans.

There will most likely be other mathematical research opportunities at Hope during this coming summer and we will highlight them in later issues of Off on a Tangent.


Problem Solvers of the Fortnight

Congratulations to Trevor Bakker, Benjamin Crumpler, James Daly, Greg Huizen and Mary DeYoung for showing that 8030! ends in exactly 2005 zeros. (There may be a ringer in this list!) Extra props to Greg for submitting his solution on the back of two ALCS tickets! Thanks, Greg, the game was great!

The solution to this problem relies on the observation that 10 = 5*2 and since there are 2s aplenty, zeros in the factorial will come from 5s. 5! = 120 provides the first zero while 10! = 3628800 ends in two zeros.  15! = 1307674368000 ends in three zeros, 20! ends in four zeros, and 25! = 15511210043330985984000000 ends in 6 zeros. Every fifth number will contain a factor of 5, every 25th number will contain two factors of 5, and every 125th number will contain three factors of 5. And so, 125!, for example, will contain 25 factors of 5, 5 factors of 25 and 1 factor of 125, giving a total of 31 factors of 5; hence 125! ends in 31 zeros. 625!, by a similar argument, ends in 156 zeros, and 3125! ends in 781 zeros. Then, since 2005 = 2(781) + 2(156) + 4(31) + 1(6) + 1, in order for N! to end in 2005 zeros we must have N = 2(3125) + 2(625) + 4(125) + 1(25) + 5 = 8030. Neato!


Problem of the Fortnight

There are 100 point-sized ants on a meter stick, distributed and oriented randomly so that they are directed toward one of the two ends. The ants travel at 1 meter per minute. When two ants collide, they reverse their orientations, and if they reach the end of the stick unimpeded, they fall off. What is the longest time before the meter stick is guaranteed to be free of ants? Write your solution on the back of a copy of the DVD A Bug's Life and drop it in the Problem of the Fortnight slot outside Dr. Pearson's office (VWF 212) by 3:00 p.m. Friday, October 28.







Got a Math Question?

Ask Elvis ...

... email him at elvis@hope.edu

Dear Friends,

You know that I like to read things other than math text books.  If fact, skiing has always fascinated me.  Since I am unable to find a pair of skis for a four legged animal, I am stuck with just reading about it.  I was reading Skiing Magazine a week ago and noticed that they have a similar column to mine.  Their column is called "Ask Dr. Flake."  He answers questions that people have about skiing or are skiing related.  A question in this month's magazine was, "What's the difference between grade (percentage) and slope (in degrees)?"

The answer to this question contained the statement, "A 100 percent grade, therefore, would be sheer vertical ..."  Any dog that knows calculus also knows that this wasn't correct.  Since grade is just slope (or rise over run) written as a percent.  Therefore, a 100 percent grade would be a 45 degree angle, not sheer vertical.  So I did what any math-conscience canine would do, and wrote a letter to the editor.  In it, I explained the problem with the response and also wrote "It seems that Dr. Flake didn't quite make the grade ..."  Kind of punny, huh?

Well you all must have been dreaming of skiing or other similar interests for the past fortnight since I have not received any questions.  (Or could it be that you were all studying for midterms?)  Don't hesitate to write me at elvis@hope.edu about your math, skiing, or other questions.  I will try to make the grade and get the answer right.




When you have eliminated the impossible, what ever remains, however improbable must be the truth.
Sir Arthur Conan Doyle (1859-1930)