# The College Mathematics Journal

### Contents for May 1999

Relating Geometry and Algebra in the Pascal Triangle, Hexagon, Tetrahedron, and Cuboctahedron. Part 1: Binomial Coefficients, Extended Binomial Coefficients and Preparation for Further Work
Peter Hilton and Jean Pedersen

As is well known, the Pascal triangle contains riches. What is not so well known is that the riches are not only arithmetical but geometrical. For example, the identity

probably would not occur to you without the aid of geometry. The triangle generalizes into three dimensions, where there is a Pascal tetrahedron.

The Bus Driver's Sanity Problem
Todd G. Will

How to minimize the time that a school bus driver has to spend with his or her passengers, measured in passenger-hours. This paper considers only the case where all of the bus stops are on one road, but one must start somewhere.

Continuous Versions of the (Dirichlet) Drawer Principle
Pawel Strzelecki

We think of Dirichlet's drawer, or pigeonhole, principle as applying only to discrete objects being placed in discrete drawers, or pigeonholes. But it has wider applicability and can be used to show, for example, that if you paint more than half of a sphere then you must have painted both endpoints of one of its diameters.

Mathematics and the Liberal Arts--II
Hardy Grant

The second part of a brief history of the place of mathematics among the liberal arts. The quadrivium of arithmetic, geometry, astronomy, and music declined in importance as the Middle Ages gave way to the Renaissance. Learning has marched on, but mathematics is still part of what educated people know, or at least once knew.

Relabeling Dice
Brian C. Fowler and Randall J. Swift

A pair of dice with faces labeled (1, 3, 4, 5, 6, 8) and (1, 2, 2, 3, 3, 4) can be used in place of ordinary dice to give the same totals with the same frequencies. There are other dice that will do the same, including an 18-sided die paired with a 2-sided one.

### Fallacies, Flaws, and Flimflam

Edited by Edward Barbeau

Let our old friend "a particle" move so that s(t) = 3t2 + 4t for 0 <= t <="3." Its average speed is the average of its speeds at t="0" and t="3." That is FFF #142 and is followed by FFFs #143-147.

### Classroom Capsules

Edited by Thomas Farmer

There are four CCs this month, including one on the average distance of the earth from the sun. There are at least four ways to calculate this number, all of which give different results.

### Media Highlights

Edited by Warren Page

The first of eighteen Media Highlights tells where on the Web you can go to trace your mathematical genealogy, if you have a Ph. D. degree. My mathematical great-grandfather is L. E. Dickson, which I didn't know until I looked at the site.

### Review

Keys to Infinity
by Clifford Pickover
Reviewed by Stan Kelly-Bootle