|OFF ON A TANGENT
|A Fortnightly Electronic Newsletter from the Hope
College Department of Mathematics
colloquia are scheduled for next week
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.
- Tuesday, April 18 at 4:00 p.m.
- VWF 102
Refreshments will be served prior to the colloquium at 3:30 p.m. in the
Reading Room (VWF 222).
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).
- Thursday, April 20 at 4:00 p.m.
- VWF 104
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
talks are by students currently conducting research under the
supervision of Prof. Nathan Tintle. This talk should be
most undergraduate students.
- Friday, April 21 from 3:30 to 4:30 p.m.
- VWF 238
In the first presentation, Laura Malpass will speak on "The Perceived
Institutional Problems Among East Coast Reformed Coast Reformed Church
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
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
- Tuesday, April 25 at 4:00 p.m.
- Science Center Atrium (tentatively)
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
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
13,111 = R (mod N)
13,903 = R (mod N)
14,589 = R (mod N)
392 = 0 (mod N) and 1078 = 0
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
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
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.
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,
|Got a Math Question?
Ask Elvis ...
... email him at email@example.com
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 firstname.lastname@example.org.
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.
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
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.
at truth, not by reason only, but also by the heart.
Pascal, Blaise (1623-1662)