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Math Horizons - September 2006


A Cantorian Tour Around the South Pole
Eli Maor

A simple geometry problem proves to be infinitely more interesting than suspected. From which point on the Earth can you go one mile south,
then one mile east, then one mile north, and end up at your starting point?

Elementary Constructions of Persian Mosaics
Reza Sarhangi and Slavik Jablan

There is the possibility that not very skilled artisans, who had no access to geometers, could create complex tile designs that require sophisticated geometric explanations. This article shows us how to create intricate tiling patterns with a few easy cuts.

A Harmonic Note
Jorge Aarao

Another random proof that the harmonic series diverges.

Manjul Bhargava: Budding Superstar
Joseph A. Gallian

The son of a chemist father and mathematician mother,  Manjul Bhargava is passionate about mathematics and classical Indian music. He is one of the youngest full professors in the history of Princeton University and an expert tabla player.

The Hyperbolic Tourist
Michael McDaniel

Visit hyperbolic (and elliptic) space where we have before us a world with many coincident parallels to a given line and another world with no parallels to a given line. After a quick tour of each, we will see a surprisingly simple connection between these worlds

How to Start...and Maintain your School's Math Club
Moshe Cohen

How to properly feed and maintain your new group of math enthusiasts. Pizza helps, but there is so much more...

International Mathematical Experiences
Robert Lewand, Robin Black, and John Hanley

Goucher College students learn about math, the kosmos, and aesthetics during an abroad experience in Greece. Others try an international summer internship working with the Umthathi Training Project in Grahamstown, South Africa

Word Wise: The Bows and Arrows of Trigonometry
Randy Schwartz and Rheta Rubenstein

The etymological roots of sine, versine, cosine, tangent, and more.

Book Reviews
Gwen Spencer and Marcus Emmanuel Barnes

Reviews of Science in the Looking Glass by E. Brian Davies and The Calculus Gallery: Masterpieces from Newton to Lebesgue by William Dunham.

Career Profile: What is an Actuary?
Jim Daniel

How and why to prepare for an actuarial career. Actuaries use mathematics, based mainly on probability and statistics, and business skills to analyze how to prepare financially for future risks.

A Journal of the Budapest Semesters n Mathematics
Emily King

A first person account of a semester abroad program in mathematics.

International Waters: An Anatomy of an Analysis
S. N. Seppala-Holtzman

Most countries adopted a fixed distance of twelve nautical miles from their coastlines as the boundary of their territorial waters. A pending proposal will increase that distance to 200 nautical miles. What would the shape of this boundary look like? Must it be exactly the same shape (but scaled up)
as the coastline, itself? Might it differ and, if so, how? To what extent did this depend upon the distance from shore that determined the boundary?

Problem Section
Andy Liu

Laura Taalman

A sudoku puzzle with a pentominological twist. Solutions available for the Pentominoku and February 2006's Hidden Crossword Puzzle and Contest.