March 2002 Contents
A Visit With Six
Monte J. Zerger
As might be expected of a small positive integer, 6 is associated with many interesting things. This paper gives some of them. For example, did you know that in dimension 3 and higher the largest number of regular polytopes is 6, occurring in dimension 4?
On Running in the Rain
Many writers have asserted that when it is raining and the wind is at your back, you should run at the same speed as the wind to minimize your wetness. This is wrong! Sometimes you should run as fast as you can.
Classifying Frieze Patterns Without Using Groups
Sarah-Marie Belcastro and Thomas C. Hull
There are only seven different kinds of symmetry a frieze pattern can have, a fact usually established using the machinery of group theory. Sheer reasoning, with no prerequisites, can give the same result.
A Tale of Two Series
Thomas J. Osler and Marcus Wright
Let us not dismiss divergent series. At times, such as the one in this paper, they can be both more accurate and easier to compute than convergent series.
Where do Functions Come From
A quick survey of the evolution of the idea of velocity, from ancient times through the Middle Ages.
It's Perfectly Rational
Philip K. Hotchkiss
The box problem (cut out the corners, fold up the sides) appears in all calculus texts. Here is how to pose it so as to get solutions in nice numbers.
Is There Enough Poison Gas to Kill the City?
On the teaching of ethics in mathematics classes. Yes, it is possible, and, the author says, desirable.
Mixed Partial Derivatives and Fubini's Theorem
Asuman Aksoy and Mario Martelli
You may not have known that Fubini's Theorem about double integrals is equivalent to the theorem about the equality of fxy and fyx, but it is.
Designing a Calculus Mobile
Instead of stacking dominoes so that the overhang becomes arbitrarily large, let us make a mobile illustrating the same principle. Here is how to do it.
Fallacies, Flaws, and Flimflam
Ed Barbeau, editor
An extension of Fubini's Theorem and other items.
Warren Page, editor
The Undying Novena
Christopher M. Rump
On the probability that a chain letter will become extinct.
The Distance Between Two Graphs
Finding the minimum distance between two curves is usually a problem in multivariable calculus, but it doesn't have to be.
The Alternating Harmonic Series
Why it converges to ln 2, and some extensions.
Using Differential Equations to Describe Conic Sections
Parabolas, ellipses, and hyperbolas have reflection properties that can be translated into differential equations.
Sums of Roots and Poles of Rational Functions
Divide one polynomial by another to get a quotient and a remainder: the sum of the zeros of the quotient is the difference of the sum of the zeros of the numerator and the sum of the zeros of the denomiator.
Problems and Solutions
Benjamin Klein, Irl Bivens, L. R. King, and Todd Will, editors
Warren Page, editor
A poem, a demonstration that the moon is really orbiting the sun, and other items.