OFF ON A TANGENT
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
December 1, 2004 Vol. 3, No. 7


Three Colloquia are scheduled in the next two weeks

Tomorrow's colloquium will focus on statistics

Nathan Tintle, a PhD student from Stony Brook University in New York, will present tomorrow's colloquium.  His title is "Reclassification as a Cost Effective Sample Design when Misclassification Errors are Present."  He will show that in certain sampling situations, the probability of misclassification of a binomial variable can be high and as the probability of misclassification increases, the power of a test of independence in a 2x2 contingency table decreases.  The traditional way to address the loss of power is to increase the sample size.  This talk compares the traditional sample design strategy (increasing the sample size) to an alternate sample design (reclassification), showing that reclassification can often be a cost effective sample design.

Join us for this talk at 3:30 p.m. tomorrow in VWF 104.  Don't forget that we will gather for Tea Time before the talk at 3:00 p.m. in VWF 222.


Do Dogs Still Know Calculus?

Tim Pennings and his sidekick Elvis (or is it Elvis and sidekick Tim?) will present a mathematics colloquium next week, Thursday, December 9 at 11:00 AM in VWF 102.  (Note the time is at 11:00 AM!)  Their talk is titled, "Do Dogs Know Calculus?" 

A standard modeling problem in calculus is to find the quickest path from a point on shore to a point in a lake where the running speed is greater than the swimming speed.  Elvis, Tim's Welsh Corgi, has never had a calculus course, but when he plays "fetch" on the shore of Lake Michigan, he appears to choose paths close to the optimal ones.  In this talk, it will be revealed what was found experimentally when Elvis was tested.  Elvis will be in the building and will be available for follow-up questions.

Colloquium will focus on statistics

Meike Niederhausen, a PhD student from Purdue University, will present a colloquium on some sort of statistic topic. (A title and abstract were not available at press time.)  Her talk is scheduled for Thursday, December 9 at 3:30 p.m. in VWF 104.  We will again plan to gather for Tea Time before the talk at 3:00 p.m. in VWF 222.


The MATH Challenge results are in

A team from Kalamazoo College won this year's MATH Challenge that took place November 6.  Taking second and third places were teams from Albion College and Bethel College respectively.  The three Hope teams finished 6th, tied for 11th, and 26th out of the 44 teams competing.


Problem Solvers of the Fortnight

Congratulations to Daniela Banu, Erin Block, Travis Dyke, Jon Oegema and Vicki Speyer, all of whom correctly determined that the most efficient way to bisect an equilateral triangle is with an arc of a circle.  To see why this is true, consider six copies of the equilateral triangle, arranged to form a hexagon.  The bisecting curves then enclose half the area of the hexagon since each encloses half of the equilateral triangle.  In fact, the exact proportion doesn't matter; we are simply looking to enclose a particular area with the curve of least perimeter, and even long before calculus was developed, it was known that the circle does the trick.

Problem solvers are invited to claim their comestible rewards from Dr. Pearson (VWF 212).

   


Problem of the Fortnight

As we usher out the old year
and look forward to the new,
we invite you to deliberate
and show that this is true:

1 - 1/2 + 1/3 - 1/4 + ... + 1/2003 - 1/2004 = 1/1003 + 1/1004 + ... + 1/2004

Submit your rhyming proof to Dr. Pearson (VWF 212) by 3:00 p.m. on Friday, December 10.  Happy holidays!


Murphy's Law Revealed

Long a piece of folkloric wisdom, Murphy's Law ("Anything that can go wrong will") has recently been quantified.  British Gas commissioned a team of scientists---a psychologist, an economist and a mathematician---to provide a mathematical equation describing this popular piece of pessimism.  They found that the probability P that something will go wrong is:



where, according to the press release, "U, C, I, S, F are coefficients between 1 and 9 representing, respectively, the urgency, the complexity and the importance of the task in question, the skill of the operator and the frequency with which the task is performed. The aggravation coefficient A was set by the committee, rather arbitrarily, at 0.7."  To read more, visit http://www.ams.org/mathmedia/.


Mathematics . . . it's elemental, my dear Mendeleev

In a random web walk, one of our field reporters stumbled across this Internet gem.  Professor Erich Friedman of Stetson University has assembled the mathematical equivalent of the Russian chemist Mendeleev's crowning achievement.  The Periodic Table of Mathematicians is available at http://www.stetson.edu/~efriedma/periodictable/.  Click on an "element" to read more about a famous mathematician (whose name usually has something to do with the representing "element").




 Got a Math Question?

Ask Elvis ...

... email him at elvis@hope.edu

Hello Elvis!

The number e is well known and is defined as the series from 0 to infinity of the function x to the k-power over k factorial. When was this definition discovered and more importantly, how long has the world known about e?

~Nykerk Musical Madman


Hello Musical Madman!

The number e is indeed a well known and beloved member of the family of transcendental numbers.  Compared to its older brother pi, e is a baby of the family, making its first, quiet appearance in 1618 in Napier's work on logarithms.  In the century or so following Napier's introduction of e, baby e grew up and made friends with many influential mathematicians, including Euler, who in 1748 published his famous result that



from which it follows that



For more information on the history of e, visit http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/e.html.

Thanks for your e-xcellent question!

 2.7182818284590-lvis


--------------------------------------------------------------------------------------------

Dear Elvis,

Why is two an odd number?  I believe that the reason has to do with algebra. Can you explain this for me?

~Susan from Minnesota

P.S.  What do you think Tim would like for Xmas this year? Send some ideas!!

Dear Susan,

The number two is the only prime number that is even.  I guess that makes two kind of odd.  This would then mean that two is the only number that is both odd and even.  That really makes it odd!

Your question reminds me of an interesting web site I saw once about special numbers.  (It seems lots of numbers are special in some way.)  You can check it out at http://www.stetson.edu/~efriedma/numbers.html.

As to you other question about Tim's Christmas present.  Believe it or not, he just loves Old Mother Hubbard's Dog Cookies.  The St. Bernard size box of those would be nice.  Also, he needs a new bed.  The one he has been looking at can be found at http://bluedogshouse.zoovy.com/product/THEE1.


  Elvis



Mathography: Lobachevsky and Hardy

Born on December 1, 1792, the Russian mathematician Nikolai Lobachevsky is most remembered for his contributions to differential equations, the calculus of variations, mathematical physics, and especially his work on hyperbolic geometry.   Visit www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Lobachevsky.html to read more about this influential mathematician.



December 1 also marks the death of noted Cambridge don G.H. Hardy, who passed away on that date in 1947.  Hardy was a towering figure in mathematics in England and Europe, and faithful readers of this column will recognize his name from the Mathography of Ramanujan, with whom Hardy collaborated.  A more detailed biography of Hardy is available at http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Hardy.html.

       

It is impossible to be a mathematician without being a poet in soul.
Sonya Kovalevsky (1850--1891)