OFF ON A TANGENT
A Fortnightly Electronic Newsletter by the Hope College Department of Mathematics
November 6, 2002 Vol. 1, No. 5

Poetry contest winners announced

Congratulations to the Math Week 2002 Poetry Contest Winners.  The first place winner was Kathryn Frens for "Calculus II."  Second place went to Priscilla Atkins for "Math: Short Takes."  Taking third place was John Siehling for "Sonnet 18 -- If Shakespeare Loved Math."  The math department's own Aaron Cinzori (aka The Commander) received honorable mention for "The Definition of the Definite Integral." The winning poems follow.
 

CALCULUS II

By Kathryn Frens

In calculus, it’s said, we add infinite things.
You laugh.
But it’s true.
When infinity stands defiant at the end of an integral,
We cower in fear in our ranks at our desks.
But our commander is bold.
Like Hector to Achilles, he offers a challenge:
single combat.
Of course, the well-armed Infinity accepts.
But watch the commander!
With a piece of chalk wielded so deftly
as to be impossible to follow, he taunts the ponderous soldier
exploiting all the chinks in his armor, avoiding the sweep of the sword.
He drops his weapon at least once in every duel.
It’s a ploy.
Infinity is overconfident, and slowly moves in for the kill,
But by then the commander has his chalk back
and with one blow reduces the foe to L.
We soldiers sit dumbfounded in our ranks.
But he is not finished yet.
Like Hector, he drags his vanquished enemy around the chalkboard
simplifying, integrating, rewriting, until
Infinity’s terrifying glory is reduced to
1/3.
 
 

Math: Short Takes

By Priscilla Atkins
 

natural numbers
march towards infinity
one by one

I imagine
mathematicians
with furrowed brows

Get real.
It’s only natural
I’m being irrational
 
 

Sonnet 18 – If Shakespeare Loved Math

By John Siehling

Shall I compare mathematics to a summer’s day?
Thou integrals are more lovely, and thou abstract algebra are more temperate:
I shall model rough winds shaking the darling buds of May using differential equations.
And the probability of summer’s lease having all too short a date:
Find the limit as hot goes to infinity of the eye of heaven,
And often mathematics can find this limit,
And although sometimes we may stumble,
It is often by chance that mathematics has taught us something new,
And this eternal wisdom shall not fade,
Nor lose usefulness in our fair world,
Nor shall death destroy the knowledge thou great mathematics,
For as we let time approach infinity, knowledge knows no limit,
So long as men can breathe, or minds can learn,
So long lives mathematics, and this gives life to thee



The Definition of the Definite Integral

By Aaron Cinzori

A definite integral's kind of a sum.
You add up rectangles -- the function they're from,
It tells you the height, and the width you can get
By cutting the interval up on a set.
That's called a partition, it starts with the 'a'
And paces off spaces 'til 'b' comes your way.
The product of height and of width is the space
The rectangle fills as it sits in its place.
The areas found by this multiplication
Are added together without innovation.
The answer you get is a sum named for Riemann.
(Not "rhyme on" but something that sounds more like "cream on.")
Now here is the thought that Bernhard called a winner:
Slice rectangles thinner and thinner and thinner.
Now look at the sums, and the limit provides
fs integral from a to b, none besides.
 

Seven students compete in the MATH Challenge

Seven Hope students competed in the Michigan Autumn Take-Home (MATH) Challenge this past weekend.  Heidi Libner, Daniela Banu, Chris VanSlooten, Ben Freeburn, Henry Gould, Michael Rininger, and James Boerkoel represented Hope College in this team event.  In groups of two or three, these students spent Saturday morning working on ten interesting mathematical problems.  We will be looking forward to finding out their results in the near future.
 

Professor Patricia Lamm from MSU to talk on "Mathematical Inverse Problems"

This week's colloquium will be given by Professor Patricia Lamm from Michigan State University.  She will present "Mathematical Inverse Problems" on Thursday, November 7 at 4:00 p.m. in VWF 104.  Professor Lamm will show that inverse problems occur widely in many applications, including problems of biomedical imaging (CT scans and X-rays), image reconstruction (from satellites or other sources), and geophysical exploration.  Using these examples, she will discuss some of the theoretical and computational challenges associated with solving inverse problems.
 

Mathematical modeling will be the topic of next week's colloquium

Anthony Tongen from Trinity International University will give a talk titled "Mathematical Modeling Applied to Materials Science" next week.  His colloquium will be presented at 4:00 p.m. on Thursday, November 14 in VWF 104.  In his talk, Professor Tongen will look at two specific areas of mathematical modeling in material science: semiconductor manufacturing and strength of metals.  He will use numerical simulations to demonstrate agreement between his models and experimental results.
 

Surfing the Web

The best place on the Web for information about the history of Mathematics is the MacTutor History of Mathematics Archive located at http://www-gap.dcs.st-and.ac.uk/~history/.  It comes from the School of Mathematics and Statistics at the University of St. Andrews in Scotland.  This site contains lots of information about mathematicians.  For example, did you know that Isaac Newton's school reports described him as 'idle' and 'inattentive' or that  Blaise Pascal's parents did not want him to study mathematics until he was 15 years old?  (Pascal defied his parents and started secretly learning about geometry at the age of 12 - crazy kid.)  The most popular biography at the site is that of John Nash, the subject of the movie A Beautiful Mind.

The MacTutor site also has information about the history of various topics in mathematics like the history of pi or the history of calculus.  It also contains the Famous Curves Index, a listing of many curves (like the Spiral of Archimedes) along with a drawing, an equation, and history of that curve.  Make sure you bookmark this site on your computer for easy reference.