Content Teasers for September 2002

## Simplicity is not Simple

While walking down a street in a remote neighborhood, we happened upon a rhombic dodecahedron in a shop window. It was a hanging lamp, in a gallery full of fantastical hip furniture.

## Geometry and Gerrymandering

Now that the U.S. Census Bureau has completed its task of counting the people of the United States, the various state legislatures will quickly be at the task of redrawing the boundaries of their representative districts. Soon after we will begin to hear cries of "Gerrymandering!"

## Who is the Greatest Hitter of Them All?

If you want to get into an argument, ask any baseball fan who the greatest hitter is. Along with emotion, bias, and hometown prejudice, you're likely to hear some statistics.

## Uncle Georg's Attic

Scattered through the attic were trunks with old carpets thrown over them, piles of cardboard boxes and brass gadgets on dusty tables, glass-fronted cupboards whose shelves were loaded with objects various and strange.

## Mashers Mathematical

"I've designed the ultimate potato-rending tool - a Hilbert masher!"

## Generalized Cyclogons

We consider a more general situation in which a curve is traced by a point z on a regular polygonal disk with n sides rolling around another regular polygonal disk with m sides.

## Row Reduction

Linear algebra: the stuff dreams are made of.

## Fighting HIV with Mathematics

For Sarah Holte, the decision to work in biostatistics was natural. "I wanted to work with some non-mathematicians and look at real-world problems." A senior staff scientist at the Fred Hutchinson Cancer Research Center, Sarah is able to do the math she loves in a diverse community of researchers and medical professionals, all investigating one of the most pressing real life problems of all: how to fight HIV.

## Problem Section

#### S-67.

Proposed by Sydney Kung, University of North Florida. If a and b are positive real numbers, prove this really cool formula (see Horizons).

#### S-68.

Proposed by Allen G. Fuller, Gordon College. Prove that for all integers n congruent to 1 or 2 mod 3, n^4 + 16 n^2 + 1 is congruent to 0 mod 9.

#### S-69.

Proposed by E. M. Kaye, Vancouver BC. If x_1 x_2 . x_n = 1 and x_i > 0, prove that for any positive integer r, (x_1 + x_2 + . + x^n)^r - x_1^r - x_2^r - . - x_n^r >= n^r -n.

#### S-70.

Proposed by Brian Williams (student), Christopher Newport University. Prove that the product from k=1 to n of (1 + n/k) is an even integer for all positive integer n.

## The Final Exam: Found Mathematics

Do you suffer from the math curse? Or have you stumbled upon mathematics in an unlikely place? Send us a photo of your "found mathematics."