The College Mathematics Journal - May 2002

articles

An Interview with Dirk Struik on the Eve of His One Hundredth Birthday
James J. Tattersall

Dirk Struik, whose most widely read work is A Concise History of Mathematics, had a long life that included, among many other things, being indicted for conspiring to teach the overthrow of the Commonwealth of Massachusetts by means of force and violence.

Nine Cubits or Simple Soma
Richard K. Guy and Marc Paulhus

If you glue together three identical cubes in an L-shape, it is possible to take nine such blocks and assemble them into a 3-by-3-by-3 cube. You or I might not be able to do it, but it is possible. You or I probably would not be able to determine in how many different ways it could be done, but that too is possible, as the authors demonstrate.

Moving a Couch Around a Corner
Christopher Moretti

Calculus teachers have been moving ladders around corners for so long that they may be tired of it. Who needs to take ladders around corners anyway? Much more practical is the problem of moving a couch around a corner. Here is how to do it.

Sums of Uniformly Distributed Variables: A Combinatorial Approach
Jeanne Albert

The idea that the density function for the sum of uniformly distributed random variables can be found by thinking about rolling dice probably has not occurred to you. Nevertheless, there is a connection

The "Origin" of Geometry
Reuben Hersh

What is an angle? Where does it exist? Hard questions! Here are two imaginary dialogues exploring them.

A Ramanujan Result Viewed From Matrix Algebra
Raymond A. Beauregard and E. R. Suryanarayan

Ramanujan found a parametric representation for solutions to the diophantine problem of expressing a sum of three squares in two different ways. It turns out that all the solutions can systematically be derived using matrices.

Winning Games in Canadian Football: A Logistic Regression Analysis
Keith A. Willoughby

To win football games, avoid interceptions and not recovering fumbles. Statistics shows, though, that interceptions are much more important. Fumble freely, but throw passes accurately!

Fibonacci Determinants
Nathan D. Cahill, John R. D'Errico, Darren A. Narayan, and Jack Y. Narayan

Fibonacci numbers don't occur everywhere but they can arise in unexpected places, such as Hessenberg matrices. (You don't know what a Hessenberg matrix is? Better find out!)

Fallacies, Flaws, and Flimflam
Ed Barbeau, editor

Continuity at a point implies continuity in an interval, and three other new FFFs.

Classroom Capsules
Warren Page, editor The Parable of the Lucky Student?
Vince Matsko

The reciprocal of the square root of x has the property that if it appears in a certain problem, students can get the right answer for the wrong reason. Luckily, there aren't many other functions with this property.

Comparing φ, {φ}, {{φ}}, etc.
Allen J. Schwenk

Here is a "physical" interpretation of {{φ}}, and even one of {{{φ}}}!

Divergence of Series by Rearrangement
Bernard August and Thomas J. Osler

How to show, easily, that a wide class of series diverges.

Almost-Binomial Random Variables
Peter Thompson

The parameter n in the binomial distribution is a positive integer. That is a constraint: what if it could be any positive integer? There are difficulties to be gotten around.

The Roots of a Quadratic
Leonard Gillman

It's tedious to substitute complex numbers into quadratic equations to make sure you've found the correct zeros. Here is a simpler way.

Fermat's Little Theorem From the Multinomial Theorem
Thomas J. Osler

At first glance, two theorems in the title don't seem to have much to do with other, but that is not the case.

Problems and Solutions

Benjamin Klein, Irl Bivens, L. R. King, and Todd Will, editors

Media Highlights

Warren Page, editor

Book Review

Stephen Smale, by Steve Batterson, reviewed by Peter Ross.