OFF ON A TANGENT
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
October 18, 2006 Vol. 5, No. 4
http://www.math.hope.edu/newsletter.html


Upcoming Colloquia

You may have been in a class when certain scores were dropped before your final grade was determined.  If we want to maximize your grade, how many scores should be dropped?  That is the question that Prof. Tom Scofield of Calvin College will answer for us in tomorrow's colloquium.

More specifically, his question is, "Given n quiz scores (not all of equal value) with r of them to be omitted from the calculation of a grade, how do we determine which r to remove so that the percentage on the remaining quizzes is maximized?"  His talk will be based on a recent paper in Mathematics Magazine.

"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!


  Join 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 students.

The Art of Mathematics lecture series continues at GVSU tomorrow night

Grand Valley State University is hosting a series of four lectures this year that will present the beauty of mathematics to a general audience. Using images to convey mathematical ideas, these talks will highlight the aesthetic qualities, diversity, and relevance of mathematics. All of the lectures are accessible to a wide audience, including students at all levels.

The second in the series of lectures is titled, "The Chaos Game and Fractal Images" and will be presented by Bob Devaney from Boston University.  In this lecture Prof. Devaney will describe some of the beautiful images that arise from the "Chaos Game." He will show how the simple steps of this game produce, when iterated millions of times, the intricate images known as fractals. He will describe some of the applications of this technique used in data compression as well as in Hollywood. He will also challenge students present to "Beat the Professor" at the chaos game and maybe win his computer.

Welcome Dorian!

If you see Professor Tintle looking a bit tired in the future, there is a simple reason for that.  He and his wife Lisa welcomed their son Dorian LeRoy Tintle into the world last Thursday afternoon.  Hopefully next semester, Professor Tintle will be sleeping through the night.

Dorian weighed 8 lbs. 5 oz. and was 20.5 inches long at birth.  (That is a little below one standard deviation above the mean for weight and a little more than one standard deviation above the mean for length.)  Congratulations to the Tintle family!

Upcoming Events at Hope 

On the morning of Saturday, October 28, several teams of Hope students will flex their mathematical muscles on The 2006 Michigan Autumn Take Home Challenge (or MATH Challenge), a three-hour exam consisting of ten interesting problems dealing with topics and concepts found in the undergraduate mathematics curriculum.  For more information about this competition and to view copies of old exams visit The MATH Challenge webpage.

Problem Solvers of the Fortnight 

Congratulations to Amanda Allen, Bill Buckman, Kevin Butterfield, Brett Jager, Chris Hall, Jackie Lewis, Jeffrey Meyers, Jeff Mulder, Jill Immink, Laura Smallegan, Martha Precup, Sarah Dix and Stephanie Pasek for correctly solving the last Problem of the Fortnight.  Adding to a growing intrigue around the department, the Anonymous Mathematician struck yet again, revealing the solution to the problem but shrouding her/his identity, leaving the editors of Off on a Tangent to scratch their heads and ask, "Who is that masked mathematician?"

The problem in the last issue was this:  Consider the polynomial p(x) = x4 - 18x3 + kx2 + 200x - 1984.  Given that p(a) = 0 = p(b) and ab = -32, find k.  Martha's solution to the problem, chosen at random from the many fine solutions we received, was this:

Since p(a) = a4 - 18a3 + ka2 +200a - 1984 = 0, we have that k = (1984 - 200a + 18a3 - a4)/a2.  Similarly p(b) = 0, and so
k = (1984 - 200b + 18b3 - b4)/b2.  Thus b2(1984 - 200a + 18a3 - a4) = a2(1984 - 200b + 18b3 - b4), and using the fact that ab = -32 we can reduce this to 3008b2 - 12032b + 12032a - 3008a2 = 0.  Multiplying both sides by a2 and again using the fact that ab = -32 we get 3080192 + 385024a + 12032a3 - 3008a4 = 0, which upon dividing by -3008 becomes a4 - 4a3 - 128a + 1024 = 0, which has two real roots a = 8 and a = -4.  Plugging either of these roots into the expression for k gives k = 86.

Problem of the Fortnight 
What is the product of the real roots of the equation

x2 + 18x + 30 = 2 (x2 + 18x + 45)1/2 ?

Here a1/2 denotes the positive square root of a.  Write your solution on the back of a pair of World Series tickets and drop them 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 351, Professor Euclid -- on your solution.


Got a Math Question?

Ask Elvis ...

... email him at elvis@hope.edu

Dear Friends,

Nobel Prizes have recently been announced.  These Nobel Laureates are honored for work that can change the course of science or benefit humanity in some great way.  There are, however, no awards for mathematics.  Mathematicians have won awards in other areas.  Perhaps most notably of recent time, John Nash won a Nobel Prize for Economics in 1994.  He even got a movie out of the deal.

Some not so prestigious awards that have also been announced recently are the Ig Nobel Prizes.  They take a more lighthearted look at science and humanity than the Nobel Awards.  For example, the 2004 Ig Nobel Peace Prize went to the inventor of karaoke.

More importantly though (as far as I am concerned) there is an Ig Nobel Prize in Mathematics.  This year the award went to Nic Svenson and Piers Barnes of the Australian Commonwealth Scientific and Research Organization, for calculating the number of photographs you must take to (almost) ensure that nobody in a group photo will have their eyes closed.  Sounds like a note worthy accomplishment.  (Though I think that pales in comparison to showing that a dog knows calculus.  Maybe next year!)

A couple of years ago someone from Spain received an Ig Nobel for Hygiene by inventing a washing machine for cats and dogs.  You've got to be kidding me!  I can understand sticking a cat in a washing machine -- in fact I dream of such things -- but a dog!  That's just wrong!

I did not receive any questions this past fortnight.  Don't hesitate to write me an email at elvis@hope.edu.  I know with midterms coming up that there must be some questions out there. 


Do not worry about your difficulties in mathematics, I assure you that mine are greater. 
~ Albert Einstein