Elvis Bogart Wales, with the
kind assistance of Professor Tim
Pennings, Hope College
Thursday, October 5
It has been
established that dogs - at least Elvis - knows calculus. That is, Elvis
can find the optimal - fastest - route to a ball thrown down the
beach and in the water. But what happens when Elvis is positioned in
the water and retrieves a ball that is also in the water? When should
he swim the entire distance to the ball, and when should he swim in to
the shore, run along the shore, and then swim back out to the ball?
What is the bifurcation point for the change in optimal strategy? Does
Elvis bifurcate? Does his fur bicate? Does Elvis buy Kate fur? Elvis will be available for follow-up questions.
Math Stories from the Hill
Professor Art White, Western
Thursday, October 12 at 4:00 pm
Professor Art White from Western Michigan University will give a
colloquium talk at Hope the Thursday after Fall Break. "I will
give personal reminiscences about students, teachers and famous
mathematicians I have known," says Professor White. "Along the
way we will try to prove that calculus is nearly pointless!"
While calculus students may have a vested interest in attending,
everyone is welcome to join us for what promises to be a very
entertaining and informative talk!
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
Events at Hope
Hope to Host
MUMC: Saturday, October 21
Registration deadline: Friday, October 13
On Saturday, October
Hope will host the 9th annual Michigan Undergraduate Mathematics
Conference (MUMC). Professor Bob Devaney from Boston University
will deliver the keynote address, entitled "The fractal geometry of the
Mandelbrot set" at 11:15 am, and students
from Michigan colleges and universities will present
findings from their mathematical research in talks throughout the
day. A continental breakfast and a lunch will be provided for
participants, and the day will conclude with a math-related game for
anyone interested. For more information and a schedule of the
day's events, please visit our MUMC webpage. To
register for the MUMC, please either sign up
on Professor Stephenson's door by Friday, October 13, or use the link
on our MUMC webpage to register. To help us ensure that we order
the right amount of food for the day, please check your calendars to be
certain you will be able to come before registering for the
MATH Challenge Just Around the
MATH Challenge: Saturday,
Sign-up deadline: Thursday,
The 2006 Michigan Autumn Take Home
Challenge (or MATH Challenge) will take place on the morning of
Saturday, October 28. 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.
The department pays the registration fee for each team and will provide
lunch to participants afterwards. The sign-up deadline is Thursday,
October 12, 2006 at 5:00 pm. Interested students can sign up by
sending Professor Cinzori an email at email@example.com
or by signing up on the list on his office door (VWF 216).
A group of students may sign up as a team. Individual students
are also encouraged to sign up; they will be assigned to a team on the
day of the competition. For more information about this
competition and to view copies of old exams visit http://www.mcs.alma.edu/mathchallenge/.
Hope College won the competition in 1997 and 2003. Let's do it
Problem Solvers of the
Congratulations to the anonymous
mathematician with no class, Ben Johnson, Beth Heisel, Brad Lininger,
Bryan McMahon, Dan Forro, Daniel Gruben, Evan Van Heukelom, James Daly,
Jeff Mulder, Jill Immink, Joel Mulder, Katie Johnson, Laura Shears,
Matt Paarlberg, Megan Patnott, Sarah Dix, Stephen Goodrich, Tiffany
Day, Tim Wahmhoff, and Tracy Albus for getting the Hamilton family
across Broom Bridge in 17 minutes! Evan Van Heukelom offered the
following creative solution:
Helen go over the bridge, taking 2 minutes. Once on the other
side, William turns around and walks over the bridge in 1 minute,
making the total time 3 minutes. With quick instruction, William
sends Edwin and Archibald back over with the lamp, bringing to total
time to 13 minutes. Once the boys are across, Mom takes off with
the lamp at the beginning of minute 13, arriving on the side William is
standing at minute 15. Mom and Dad then return to their kids on
the other side of the bridge. On their romantic talk alone, they
discuss the thought of not having any more kids because it is beginning
to take too long to get to church. So 17 minutes after beginning
their bridge excursion, the trip has been concluded. And it was
now time to go to church. While sitting in church, William was
trying to figure out a faster way home because he really had to use the
bathroom. He concluded that there was no quicker way, but in his
attempt to distract himself from his bladder, he thought of a way to
generalize the complex numbers to higher dimensions. And rather
than writing the equations in his hymnal, he wrote them on the bridge
while waiting for his children to cross on the way home. He then
went home, had dinner and rested his legs after an exhausting walk to
Problem of the
Consider the polynomial
p(x) = x4 - 18x3 + kx2 + 200x - 1984
Given that p(a)
= 0 = p(b) and ab = -32, find k.
Once you've found the value for k, graph the polynomial p(x)
and write your solution (not just the value of k, but how you determined it)
on the back of your graph and drop it in the Problem of the
Fortnight slot outside Professor Pearson's office (VWF 212) by 3 pm on
Friday, October 13. Please be sure to include your name, your
math class(es) and the name(s) of your professor(s) -- e.g. Ima
Student, Math 131, Professor Isaac Newton -- on your solution.
Got a Math Question?
Ask Elvis ...
... email him at firstname.lastname@example.org
I have a couple of questions to answer
this week about soccer.
Though one is really about mathematics. If you have any questions
about math or the sport of your interest, send me an email at
email@example.com. I hope to hear from you!
have seen you at a number of
Hope College soccer games, so I have a
question for you about soccer/math. The Hope team uses the
traditional soccer ball made up of hexagons and pentagons.
However, in the World Cup this year, I noticed that the ball was
different. There weren't any hexagons nor pentagons to be found
on the entire ball. What do you think of this new less
I don't know about the new ball being
less mathematical. It is
just different mathematically.
might call the traditional soccer ball a truncated
icosahedron. It consists of 32 polygonal regions---20
hexagons and 12 pentagons. This, of course, is a
polyhedron with flat sides. The folks that make soccer balls,
however, fill them
up with air and it make an object that is pretty close to a
sphere. (By the way, did you know that in 1996, the Nobel Prize
in Chemistry was awarded to three chemists, one a Hope alumnus, for
their discovery of a
carbon molecule that has the shape of a soccer ball? I wonder
what shapes they are now looking for. Golf balls?
Cats? That would be interesting!)
The new soccer ball made by Adidas does
not consist of any polygons,
but is constructed with two different types of curved panels.
Since these panels are no longer polygons, one might think that this
ball is less mathematical. However, in the branch of
mathematics called topology,
mathematical shapes can be preserved even when they are stretched
and twisted. In other words, we can take a circle and smoosh it
like a piece of dough and have it become a pentagon, but topologically,
the shape hasn't changed. We change shape by poking a hole in it
and frying it up into a doughnut. Looking at the new soccer ball
can make it a truncated
octahedron made up of eight hexagons and six squares. Pretty
Therefore, I wouldn't say that it is
less mathematical, but just has
different mathematics. I still prefer the more traditional soccer
ball, however. After all, you know what they say about old dogs
and new soccer balls!
play a lot of soccer and while
I have shin guards and shoes to
protect my feet, I have nothing to protect my head. (I tend to
use my head a lot and some people think I use it a bit too
much!) Don't you think that there ought to be some kind of head
protection for soccer players?
While I have never seen one, there are
different head protection
devices made for soccer players. You can see a picture of one here.
I have seen soccer players heads run
into a variety of objects, so it
would make sense that one's head could use a little protection.
However, Z.Z., if you do wear head protection playing soccer, I
would suggest that you not run your head into anything that you should
not run your head into! I think you know what I mean.
It is not knowledge, but the act of
learning, not possession but the act of getting
there, which grants the greatest enjoyment.
~ Carl Friedrich Gauss