A relation between Catalan Numbers and World Series type problems

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**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 theJournal.)

**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 theJournalit 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.

**Centering**

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 3^{a+b}=3^{a}+3^{b}, and other items.

**Classroom Capsules**

Tom Farmer, editor

**Proofs Without Words Under the Magic Curve**

Füsun Akman

Sketch a graph of y = 1/xand 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 midpointM. Then, if the curve is nice, it has a pointCon it whereMCis perpendicular to the tangent line atC.

**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.

Irl Bivens and Ben Klein, editors

Warren Page, editor

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