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The College Mathematics Journal - January 2002


Was Calculus Invented in India?
David Bressoud

Well, no, actually it wasn't, but two hundred years before Newton and Leibniz some Indian astronomers came very close, deriving series expansion for the sine, cosine, and arctangent. Alas, their work died out in India, but here is how they did it.

Is Presidential Greatness Related to Height?
Paul M. Sommers

Well, yes, actually it is. The taller you are, the more likely you are to be a great president, or so statistics shows. (There will be only one more question asked by a title in this issue of the Journal.)

Perfecting the Analog of a Deck of Cards, or Why Evolution Can't be Left to Chance
J. G. Simmonds

Here is a simple model of evolution that shows how surprisingly quickly a favorable mutation can spread throughout a population.

Cantor, 1/4, and its Family and Friends
Ioana Mihala

In a previous paper in the Journal it was shown that 1/4 was an element of the Cantor set. Since the set has uncountably many elements, there are quite a few others but they tend not to be familiar. Here are some, not uncountably many, but old friends like 1/12, 1/13, and 1/28.

Jim Sauerberg and Alan Tarr

A new geometric transformation: given a point in a finite set of points, move it to the center of the circle determined by its three nearest neighbors. The operation has many properties. For example, given a parallelogram, sometimes its area will decrease when its points are centered and sometimes it will increase. Guess which parallelograms do which. Give up? If the parallelogram has an angle less than 45 degrees, it will shrink toward nothingness.

Hat Derivatives
Stephen B Maurer

The hat derivative of a product is the sum of the hat derivatives of its factors, a pleasant property and one that arises naturally when percentage changes are of interest, as they often are.

Fallacies, Flaws, and Flimflam
Ed Barbeau, editor

A proof that if a function is continuous at a point then it is continuous in an interval around that point, an application of 3a+b=3a+3b, and other items.

Classroom Capsules
Tom Farmer, editor

Proofs Without Words Under the Magic Curve
Füsun Akman

Sketch a graph of y = 1/x and you have all the properties of the logarithm function, and then some.

On a Mean Value Theorem
Peter R. Mercer

Take a curve, draw a secant line, and find its midpoint M. Then, if the curve is nice, it has a point C on it where MC is perpendicular to the tangent line at C.

Symmetric or Skewed?
Joseph G. Eisenhauer

Mean, median, and mode: they can, of course, occur in any order. But what if our distribution is skewed? Then we must know something about the order in which the measures of central tendency must appear, mustn't we? No, we mustn't.

Elementary Linear Algebra and the Division Algorithm
Airton von Sohsten de Medeiros

The division algorithm in the ring of polynomials over a field.

Some Calculus-Based Observations on the Solutions to x" - q(t)x = 0
Allan J. Kroopnick

If one solution is unbounded and the other is bounded, then the bounded solution can be found from the unbounded one.

Problems and Solutions

Irl Bivens and Ben Klein, editors

Media Highlights

Warren Page, editor

Book Review

The Shape of the Great Pyramid by Roger Herz-Fischler, reviewed by Frank Swetz.