# The College Mathematics Journal

### September 2002 Contents

Spanish Colonial Mathematics: A Window on the Past
Edward Sandifer

It may not be generally known that the first mathematics book published on this continent appeared in 1556, significantly before the Pilgrims encountered Plymouth Rock, and much before 1703, when the first mathematical work in English was published. This article surveys the contents of some early books.

A Generalized Chinese Remainder Theorem
Fredric T. Howard

A method used for solving simultaneous congruences when the moduli are relatively prime is here generalized to moduli that have common factors.

Can a Bicycle Create a Unicycle Track?
David. L. Finn

Sherlock Holmes once deduced something or other important from observing the track of a bicycle. He was lucky. It is possible for a bicycle track to be indistinguishable from that of a unicycle, though it would be difficult for a bicycle rider to create one, especially if pedaling away from the scene of a crime.

Chasing Hank Aaron’s Home Run Record
Steven P. Bisguier, Benjamin S. Bradley, Peter D. Harwood, and Paul M. Sommers

Babe Ruth hit 714 home runs and Hank Aaron 755. Will we see that record surpassed in our lifetimes? The authors conclude that it’s likely that we will, if we, and the home-run producers, can stay healthy for another few years.

When is 1/(a + b) = 1/a + 1/b, Anyway?
Eugene Boman and Frank Uhlig

The Law of Universal Linearity, of which the equation of the title is a special case, is not to be depended on. However, it sometimes holds, and this paper gives some instances.

A New Look at Probabilities in Bingo
David B. Agard and Michael Schakleford

In a bingo game with 100 cards in play, how many numbers must be called before there is a better than even chance that someone will yell, “Bingo!”? After you guess and get the wrong answer, you may use this as a test of bingo-intuition to annoy your friends and loved ones. The answer is 16. Several other bingo questions are answered too.

A Very Brief History of Statistics
Howard W. Eves

Two and a half pages do the job.

Fallacies, Flaws, and Flimflam
Ed Barbeau, editor

A problem from the Florida Math Olympics: “If x > 0 and x + 1/x = 1, then evaluate x2 + 1/x2.” Tricky!

Classroom Capsules
Warren Page, editor

Introducing Binary and Ternary Codes via Weighings
James Tanton

Convergence-Divergence of p-Series
Xianfu Wang

A new way to determine an old result.

Observations on the Indeterminacy of the Sample Correlation Coefficient
Owen Byer

When y > 2, the correlation coefficient for {(1,2), (2,2), (3,2), (4,2), (5,2), (6,y)} is .655… for all y. Surprised?

Exact Values for the Sine and Cosine of Multiples of 18º

Exact values, full of square roots of 5, from pictures.

Obtaining the QR Decomposition by Pairs of Row and Column Operations
Sidney H. Kung

Another way, not involving the Gram-Schmidt process.

The nth Derivative Test and Taylor Polynomials Crossing Graphs
David K. Ruch

How to tell if the graph of a function’s Taylor polynomial crosses the graph of the function.

Problems and Solutions

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

Media Highlights

Warren Page, editor

Book Review

Hidden Unity in Nature’s Laws, by John C. Taylor, reviewed by Jet Wimp.