A note from our fearless leader Peter Andrews:

If you have been in the lounge this morning you will have seen the bread
laid out on the table as a reminder that our end-of-term party is coming
up this afternoon. I hope you will all be able to come by for at least
a short while and preferably a long while!

As you probably know, Bert Reed and Greg Ronsse are both retiring at the
end of this term. Greg has stated publicly that he will be back a few times
in the spring and that he would rather we held any formal recognition until
sometime in the spring. I'll keep you posted.

If there are any others of you planning to retire in the next 3 weeks,
please let me know!!

Take a whiff of the bread and come by the center tower at 4:00 to sample
each loaf -- and then some!!

Thanks for another term -- furlough free!! Happy Finals, Happy Grading,
and finally Happy Holidays.

Anyone within the sound of this message is invited to attend.

James Garfield's Proof of the Pythagorean Theorem

James Garfield, the 20th President of the United States, gave the following simple proof of the Pythagorean theorem



It begins by constructing the trapezoid with parallel sides of height a and b and with base a + b. The area is given by the base times the average height or

A = (1/2)(a+b)².

On the other hand, we may compute the area of the three nonintersecting interior (and necessarily right) triangles

A = (1/2)(ab + ab + c²),

where c is the hypotenuse.
Setting up the equation for the two equal area calculations we have


(1/2)(a² + 2 a b + b²) = (1/2)(2 a b + c²),

or
a² + b² = c².

Yevgenia Movshovich to Give December 4th Colloquium

Yevgenia Movshovich will give the final coloquium of the semester today.

A pdf abstract can be found on the department website
The talk will concern positive harmonic functions on Dirichlet domains.

Suhrit Dey to Give Friday November 13th Colloquium

Professor emeritus Surhit Dey will talk at 4 pm. Friday November 13th about stiff systems. The talk will attempt to explain certain natural phenomena of perception.

There Once was a Fellow Named Gauss

There once was a fellow named Gauss
whose scholarly peers could not grouse
of his genius elan
on which he had drawn
for his manifold curvature blouse

Scott Tichenor of the University of Illinois to Give November 6th Colloquium

Scott will give a short introduction concerning curves of constant width and provide examples. He will also show how to construct these curves.

Gregory Galperin Discusses Rational Dissection of Polygons

Professor Galperin discussed the problem of dissecting a pentagon using the diagonals as shown.


The first question is whether the areas a1,a2,...,a10 taking rational values implies that the area a11 is a rational number. The answer is that it does. But more surprisingly, we need only a1,a2,...,a9 to take rational values in order to imply that the areas a10 and a11 take rational values.

Professor Galperin was able to show that it is only necessary that 5 consecutive triangles have rational areas in order to show that all of the dissected areas are rational for the pentagon. In addition, he indicated how the result generalizes.

Professor Galperin to give October 30th Colloquium

Gregory Galperin will give the Friday afternoon colloquium this week.

He will discuss the dissection of polgons. In particular, if you dissect a polgon using the diagonals and the triangular pieces have rational area, what can be said of the inner piece?

Darin Johnson Gives Lecture on Rook Polynomials

The rook problem is related to the number of nonattacking rooks that can be placed on a Ferrers Board. A Ferrers board is a board in which the number of cells in a column is always nondecreasing from left to right until it terminates. A rectangular board is a simple example of a Ferrers board.

Dr. Johnson showed how the Rook problem on the Ferrers board generates various polynomial coefficients which are in turn related to several examples of well known number sequences in mathematics and combinatorial number theory.

It's How One Sees The World

An Area Restaurant?

Gina's Pies Are Square Restaurant in Wilton, Wisconsin. Does this mean that cornbread are round?

The reference is to the old joke about the hayseed helping his son with his homework. He asks his son for the area of a circle and his son responds with Pi R squared to which his father replies,
No, no, son, pie are rounded, cornbread are squared.

Dr. Darin Johnson to Talk at October 23rd Colloquium

Darin Johnson (EIU B.S. Comp. Sci. and M.A. Mathematics graduate) will give the October 23rd colloquium talk. He will discuss the Generalized Rook Problem.

Newtonian Mechanics?

Despite the image of Issac in overalls, Newtonian mechanics is not so much about fixing automobiles as it is about how automobiles move in space. Issac Newton laid down the basic principles of motion. Namely, 1) a body in motion tends to stay in motion unless acted upon by an outside force, 2) the applied force is equal to the mass times the acceleration, 3) for every action there is an equal and opposite reaction.

..and when the teacher told Tommy to write a sentence about Issac Newton, Tommy wrote I sack a new ton of potatoes every day.

Professor Delman's Friday Colloquium

Professor Delman gave the department colloquium talk on October 16th. The talk concerned some recent work by Lenhard Ng. Professor Ng uses the connected paths between pairs of points on a knot to construct formal polynomial rings. Equivalence classes for certain topological operations are introduced which produce the so-called Cord Ring. Professor Delman indicated how one could compute the Cord Ring for certain kinds of knots such as those that can be constructed on the surface of a torus

Charles Delman to Talk on Knots at October 16th Colloquium

Lenhard Ng introduced a knot invariant in 2005 called the cord ring invariant. Professor Delman will discuss the properties of this invariant and some work in progress.

October 2nd Colloquium by Peter Andrews

Peter Andrews gave the colloquium talk on Friday October 2nd at 4 p.m.

The purpose of the talk was to introduce the faculty to a new package of free software called Geogebra which can be used for geometric demostrations.

An example of its use was given by showing that every conic section could be defined as the set of points equidistant from a fixed point and a moving point on a circle (including the circle at infinity, i.e. a straight line).

Professor Andrews also discussed Archimedes' measurement of the ellipse and parabola using Geogebra to demonstrate certain relations not easily obtained.

We're Off Like a Herd of Turtles

This project is an attempt by the Mathematics and Computer Science Department at Eastern to use the facilities of the www to interact with our friends and alumni. We encourage you to add comments or email us at eiumath@gmail.com or anyone at the department. The department hosts a regular website at www.eiu.edu/~math which contains faculty and staff email adresses and information about the academic side of the department.