The College Mathematics Journal - March 2006

March 2006 Contents

ARTICLES

Truck Drivers, a Straw, and Two Glasses of Water
Kevin Iga and Kendra Killpatrick
82-92
While waiting for his meal to arrive, a truck driver was using his straw to move water from one glass to another when he was struck by this question: If I keep doing this, will the two glasses ever have exactly the same amount of water? This article looks at various problems related to that question.

Straw in a Box
Richard Jerrard, Joel Schneider, Ralph Smallberg, and John Wetzel
93-102
A problem on a state's high school exit exam asked for the longest straw that would fit in a box. The examiners apparently wanted the length of a diagonal of the box, but the figure accompanying the question suggested otherwise — that the radius of the straw be considered. This article explores that more general problem.

A Card Trick and the Mathematics Behind It
Gabriela R. Sanchis
103-109
We describe a card trick in which the magician is able to identify correctly a card chosen randomly from an array of cards by a member of the audience. We then explore the mathematics behind the trick.

No Arithmetic Cyclic Quadrilaterals
Raymond A. Beauregard
110-113
A quadrilateral is arithmetic if its area is an integer and its sides are integers in an arithmetic progression, and it is cyclic if it can be inscribed in a circle. The author shows that no quadrilateral is both arithmetic and cyclic.

Folding Beauties
Leah Wrenn Berman

How to View a Flatland Painting
Mark Schlatter
114-120
Using the problem of determining where a Flatland artist was standing, this article takes another look at perspective.

Fallacies, Flaws, and Flimflam

Ed Barbeau, editor 121-124

Classroom Capsules

Michael Kinyon, editor
125-142

The Birthday Problem Revisited
Eric Maim, Gail Nord, James Colin Hill, and John Nord
125-128
The birthday problem considered here is that of having been born on a specific date, say January 1, not just one person, but precisely k in a group of n. Extending the probability to being continuous through the use of the gamma function leads to an interesting surface.

A Geometric Look at Sequences that Converge to Euler's Constant
Duane W. DeTemple
128-131
In this note, the author generates and then investigates further some sequences that converge to Euler's constant.

Partial Fraction Decomposition by Division
Sidney H. Kung
132-134
The author shows how division can be used to find the partial fraction decomposition of a rational function whose denominator is either a power of a linear function or a power of an irreducible quadratic.

An Elegant Mode for Determining the Mode
D.S. Broca
134-137
A method first proposed by N.A. Rahman uses the logarithm and the derivative to find the mode. The technique is illustrated for three skewed density functions, the extreme value, the Weiball, and the lognormal.

Searching for Möbius
Al Cuoco
137-142
This capsule shows the Möbius function arises through the algebra of formal Dirichlet series.

 

Problems and Solutions

Media Highlights

Book Reviews

George Pólya Winners