OFF ON A TANGENT
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
April 12, 2006 Vol. 4, No. 12
http://www.math.hope.edu/newsletter.html

Three colloquia are scheduled for next week

The Fundamental Theorem of Algebra: History, Proofs, and Applications
The Fundamental Theorem of Algebra dates back to the mid-17th century, and it can be stated quite easily: every polynomial with complex coefficients has a complex number as a root.  There are numerous modern proofs of this theorem, drawing on such diverse fields as complex analysis, abstract algebra, and topology.  In this talk, Ryan Higginbottom from Kalamazoo College will discuss at least two of these proofs and he will touch on some of the theoretical applications.  This presentation should be accessible to anyone who has completed Calculus I. 

Refreshments will be served prior to the colloquium at 3:30 p.m. in the Reading Room (VWF 222).

Algebraic Topology
 Alice Wang from Michigan State University will be here next week Thursday to speak on a topic from algebraic topology.  Refreshments will be served prior to the colloquium at 3:30 p.m. in the Reading Room (VWF 222).

Research about the Reformed Church in America
 A series of three short talks will be given as a single colloquium presentation next week Friday.  All three talks are by students currently conducting research under the supervision of Prof. Nathan Tintle.  This talk should be accessible to most undergraduate students. 

In the first presentation, Laura Malpass will speak on "The Perceived Institutional Problems Among East Coast Reformed Coast Reformed Church in America Members and Adherents."  In the second, Jennifer Rice will answer the question "Does religious denomination of one’s youth affect participation and beliefs?"  She will use results from the East Coast Reformed Church in America lay persons survey.  Finally, Elizabeth Hammon, Kathleen Harper, Laura Nettleton and Sara Stevenson will give a report on "The impact of geopolitical, religious and institutional context on membership growth and average worship attendance in the Reformed Church in America: 2000-2004."


The Klein Four Group will be performing at Hope

Last fall we reported about a mathematical a cappella group from Northwestern University, The Klein Four. They will be including Hope College as a stop on their "Spring 2006 Tour."  They recently released a CD titled Musical Fruitcake. It includes such songs as "Finite Simple Group," "Lemma," "Contradiction," and "Mathematical Paradise." As you can see, their songs are mathematically related and are quite humorous.

You can check out their website at http://www.kleinfour.com. From there, you can view some of their musical performances as well as other productions, buy their CD and other merchandise, view their bios, and get more information about this interesting group.


The Klein Four Group


The LMMC results are in

The Lower Michigan Mathematics Competition took place earlier this month here at Hope.  Thirty-five teams from 11 colleges and universities in Michigan participated in trying to solve ten interesting problems.  A team from Ferris State University finished in first place, while teams from Grand Valley and Albion finished second and third.  Hope's highest ranking team, consisting of Kurt Pyle, Benjamin Crumpler, and James Daly finished in fourth place.  A team from Calvin rounded out the top five.

Teams from Hope have won the competition 10 times in it's 30-year history, most recently in 2003.

Hope was represented by 35 students organized into 12 teams.  The other participating Hope students were:  Brian McLellan, Brian Wyns, Erik Ladomersky, Jackie Lewis, Chris Hall, Vidhan Rana, Nathan Johnson, Ryan Johnson, Bryan McMahon, Jacob Lyons, Mark Panaggio, Brian Straw, Bo Buckley, Ricky Kelly, Zach Hoernschemeyer, Parth Patel, Kyle Eurick, Andrew Abela, Megan Patnott, Kim Harrison, Sarah Story, Ben Mannino, Betsy Carlson, Patrick Mears, Katie Johnson, Heather McGovern, Katie Henveveld, Sam Rossman, Laura Shears, Joy Taylor, Lucas Osterbur, and Yoshiya Hikita.


Problem Solvers of the Fortnight

Congratulations to Stephanie Allen, Jeff Ambrose, Kevin Browder, Bart Bultman, James Daly, Greg Huizen, Mark Humberstone, Clint Jepkema, Forrest Gordon, Jackie Lewis, Dan Lithio, Bryan McMahon, John McNutt, Patrick Mears, Jon Moerdyk, Keith Mulder, Stephanie Pasek, Megan Patnott, Martha Precup, Jennica Skoug, Billy Statema, Sean Thurmer, Dirk Van Bruggen, Paul VanderVelde and Ben Worrel for figuring out that 98 was the greatest common divisor of the three numbers 13,511, 13,903 and 14,589 that leaves the same remainder. 

There were many creative approaches to this problem; one nice way is to think of these three numbers as long 1 x n blocks.  Then we're looking for the number N (a 1 x N block) that will go into these numbers a certain number of times (different for each number) and leave the same remainder R (a 1 x R block).  Then the difference between any two of these numbers will also be divisible by N (because each will contain one 1 x R block), and so we are looking for the greatest common divisor of 392 (= 13,903 - 13,511) and 1078 (= 14,589 - 13,511).  A factor tree of each of these reveals the greatest common factor as N = 2(7)(7) = 98.

For those who know a little modular arithmetic, we are solving the system

13,111 = R (mod N)
13,903 = R (mod N)
14,589 = R (mod N)

and so

392 = 0 (mod N) and 1078 = 0 (mod N)

from which we get N = 98.  (The remainder R, which happens to be 85, plays no role in solving this problem.


Problem of the Fortnight

Two perpendicular chords intersect in a circle.  The lengths of the segments of one chord are 3 and 4.  The lengths of the segments of the other chord are 6 and 2.  Find the diameter of the circle.

Write your solution on an official Rawlings baseball signed by Pudge Rodriguez (actually, a picture of a baseball will suffice) and drop it in the Problem of the Fortnight slot outside Dr. Pearson’s office (VWF 212) by 3 p.m. on Friday, April 21.


So They Tell Me
By JENNICA SKOUG | Poet in Residence

…that 2+3=5,
that parallels never cross,
and infinity is more than you can count.
…that numbers are real, solid things;
    nothing questionable here.
Math is self-containing facts.  Logical
facts that make sense.
Math doesn’t lie, provided
    you follow the rules.

But math can lie, and does –
or mathematicians do.
    Done any statistics lately?
Life’s a matter of chance, anyway.
    Nothing’s certain;
    the laws of the universe
    are an exercise in probability.
Is there a cut-off line for truth?
Take Schrödinger’s paradox: no half-dead cats allowed.
If our cat is the truth, is 90% good enough?
Cat or truth, alive or dead,
there’s no finding out until you
    open the box.

I’m still working on mine.
The lid seems to be stuck in places.
In the meantime,
they’ve told me
that infinity is countable (sometimes),
that parallels cross (on spheres),
that a number’s only real if
    it’s not imaginary,
and in mod 4, 2+3=1.

I passed calculus,
    where bold protests rang,
“This has a fun factor of cos(pi/2)!”
(that was freshman year)
And just when I thought I knew everything,
There was Proof class, Analysis, Topology
    with arbitrary functions
    and spaces that have no form unless you form them,
    where strange things happen
    and they look at you and say,
“It doesn’t make sense!
That’s why it’s so cool!”
I looked up once and said, “wait –
    who’s making the rules here?”
And smiling, they said,
    “You are.”



 Got a Math Question?

Ask Elvis ...

... email him at elvis@hope.edu


Dear Friends,

My "tail" has been wagging faster than usual the past week.  Part of it has to do with the warmer weather we have been having.  With that warm weather, Mittens, the cat that lives next door to me has been outside more often. While chasing squirrels is fun, chasing Mittens is pure joy.  I think I treed her five times last week.

Also contributing to my increase in tail wagification was the fact that I finally received a question to answer.  This gave me something to do on my long days in the office.  Remember if you have a question for me, don't hesitate to write me at elvis@hope.edu.




all right, Elvis, I have a question, and here it is:

Just how many cups of coffee does Dr. Mark Pearson drink per day?  If I have never seen him without a mug by his side, can I infer that his consumption of this energizing beverage is, perhaps, infinite? Could we create a formula to predict just how much coffee this enthusiastic professor consumes on any given day of the year?  With your aptitude for applied mathematics (and because I've noticed you hang around his office a lot), I thought you could help me out.

Sincerely,
Contemplating Coffee


Dear Contemplating,

The famous mathematician Paul Erdős is quoted as saying "a mathematician is a machine for turning coffee into theorems."  Do you think that that is what Dr. Pearson is up to?  Or is he turning coffee into exams and assignments?  I too have noticed that a coffee mug was frequently in his hand or by his side.  A thorough investigation into his potential drinking problem was in order.  After all, what else do I have to do.

I first got some background information on coffee consumption.  Did you know that about 54% of the adult population in the U.S. are daily coffee drinkers?  Of these coffee drinkers, the average consumption is 3.1 cups of coffee per day.  However, the coffee consumption in Sweden is more than twice that in the U.S. on a per capita basis.  So we may conclude from this that Dr. Pearson may be genetically predisposed to abuse this addicting drink.

The next thing to do was to go undercover and observe his drinking behavior for a week.  I decided that I would play the part of a dog looking for a handout while secretly taking careful mental notes of Dr. Pearson's drinking behavior.   I found that he did in fact exceed that average American coffee drinkers consumption each day (though not quite up to the amounts of those caffeine-craving Swedes.)  However, here is the most disturbing part of my findings.  Sometimes his mug is not filled with coffee, but with other dark stimulating beverages namely tea and Pepsi.  The good news is that I have yet to see him with any Red Bull or SoBe No Fear in his hands.

So while his caffeine consumption might seem excessive by American standards, I guess it is fairly low for a Swedish mathematician---as long as he puts the power of caffeine to good use, and doesn't turn to the dark brewed side.

Elvis


We arrive at truth, not by reason only, but also by the heart.
Pascal, Blaise (1623-1662)