# The College Mathematics Journal - November 2001

### ARTICLES

Estimating Large Integrals: The Bigger They Are, The Harder They Fall
Ira Rosenholtz

You probably have never felt the need to evaluate a really big integral, something along the lines of exp(exp(x)) times some large power of x, from 0 to, say, 1,000,000. Even so, we should not let monsters like that roam around untamed. This paper gives an easily-remembered method of subduing them.

CORDIC: Elementary Function Computation Using Recursive Sequences
Neil Eklund

Using a single family of recursion relations, it is possible to calculate products, quotients, sines, cosines, arctangents, square roots, hyperbolic sines and cosines, logarithms, exponentials, and hyperbolic arctangents. That's the way computers do it.

Conformality, the Exponential Function, and World Map Projections
Timothy G. Feeman

When Mercator set about representing the sphere of our planet on a sheet of paper in 1596, he decided that it was important that angles be preserved, and so they are in the Mercator projection. Stereographic projection is conformal as well, as is exp(z). We can have conformal projections of hyperboloids too, if we want them.

In Search of a Missing Link: A Case Study in Error-Correcting Codes
Andy Liu

A natural progression from including a single parity-check bit in a message to the Hamming-Golay error-correcting code, as found by the author's pre-college students. As always, hindsight shows how natural and inevitable it is.

The Profit in Being Unbalanced
Wolf von Rönik

Currency exchange rates can present opportunities for sure profits, if you can find them and act quickly enough. All you have to do is identify unbalanced matrices. Warning: if you lose your shirt trading dollars, yen, and euros, the Journal will not make good your losses. On the other hand, contributions from accumulated profits are always welcome.

Dipsticks for Cylindrical Storage Tanks - Exact and Approximate
Pam Littleton and David A. Sánchez

Given a horizontal cylindrical storage tank, it would be handy to have a dipstick with marks indicating 1, 2, ... gallons (or 100, 200, ... for bigger tanks). Where to put the marks? Here's how to do it.

Geometric Progressions - A Geometric Approach
Michael Strizhevsky and Dimitry Kreslavskiy

How to make pretty pictures of some geometric progressions (the first author teaches at the Art Institute of Atlanta) and, incidentally, to verify that cot(a/2) = (sin a)/(1 - cos a).

Fallacies, Flaws, and Flimflam
Edited by Ed Barbeau

Some functions with two different antiderivatives, a proof that the cardinality of the class of subsets [0, 1] is the same as the cardinality of [0, 1], and other items.

### Classroom Capsules

The Logarithm Function and Riemann Sums
Frank Burk

Riemann sums with unequal subintervals have their uses, among which is showing what happens to n(a^(1/n) - 1) as n increases.

An Application of L'Hôpital's Rule
Jitan Lu

A student's clever but erroneous application of L'Hôpital's Rule turns out to be all right after all.

The Attraction of Surfaces of Revolution

What is the force exerted by a massive surface of revolution on a point mass located on the axis of symmetry? Assuming an inverse square law of attraction, of course. Here is the answer.

An Elementary Approach to ex
John W. Hagood

Let e be the unique real number larger than 1 such that xe-x is greatest when x = 1. This unusual definition has advantages.

Why It Might Seem That Christmas Is Coming Early This Year
David Strong

Time, alas, moves faster as we age. This universal perception can be quantified, though nothing can be done to slow the passage of the years.

Sum Rearrangements
Russell A. Gordon

How to make series add up to anything.

Generating Functions and the Electoral College
Christopher Stuart

The chance of having a tie in the electoral vote for president is small enough so that we don't have to worry about it.

### Problems and Solutions

Edited by Benjamin G. Klein, Irl C. Bivens, L. R. King, and Todd G. Will Student Research Project
Jack E. Graver and Lawrence J. Lardy

Enclosing fields with fences is a constant activity in elementary calculus. The problem has several variations that can be investigated.