You are here

Math Horizons - February 2005


Pi Day
Joanne Caniglia & Barbara Leapard 

Celebrating p begins on 3/14 at 1:59 p.m. each year at Eastern Michigan University.

A Dozen Questions About Fibonacci Numbers
James Tanton

2, 3, 5, 8, who do we appreciate? Fibonacci! Fibonacci! Fibonacci!  Your dozenal correspondent views Fibonacci numbers as classic square-domino tilings, honeycomb walks, ordered partitions, restricted permutations, and more. Come explore this fascinating number sequence.

Integers Causing Bipolar Orientation Reversal of Appendage Motion
Colin Adams

"While sitting are your desk, lift your right foot off the floor, and make clockwise circles. Now while doing this, draw the number "6" in the air with your right hand. Your foot will change direction and there's nothing you can do about it." ---Widely distributed e-mail.

This mathematical exploration will quite literally have you spinning in circles. An integer is bipolar if its air depiction causes a rotating foot to switch direction (regardless of the direction of rotation). So which integers are bipolar?

One in Two, Two in One: Mathematics and the Arts
Carla Farsi & Doug Craft

Mathematics and art are related endeavors. What mathematician has not marveled at the beauty of an elegant proof and what serious artist has not been aware of the importance of form and composition to a successful art work? This article discusses the similarities and differences between these two endeavors, while celebrating successful collaborations of Denver area mathematicians and artists.

A Conversation with Leonardo Pisano
Ezra Brown

A Math Horizon's exclusive interview with Leonardo Pisano, AKA Fibonacci.  Learn why he introduced the west to "Indian figures", "zephir", and "al-jabr" in his book Liber Abaci. Hear his account of an imperial contest. And heed his excellent advice for current students of mathematics.

A Mathematician's Look at Foucault's Pendulum
Stuart Boersma

Strip away the physics and Foucault's Pendulum is nothing more than a calculus problem posed on a sphere. Since some of Einstein's work equates the mathematical quantity, curvature, with the physical quantity, matter, it makes sense to tackle the familiar pendulum problem from a completely mathematical formulation.

A response to this article by Greg Johnson (added June 2005).

Alumnae Profiles: Wellesley College
Megan M. Kerr, Alan Shucat, & Ann N. Trenk

A women's college with a strong tradition of liberal arts education. Famous alumnae include Mayline Soong (Madame Chiang Kai-shek) '17, former Secretary of State Madeleine Albright '59, Senator Hillary Rodham Clinton '69, and Space Shuttle pilot Colonel Pamela Melroy '83. Read profiles of mathematics students Katie Gottshall '03, Beth Pontius '03, Christine Murashige '97, Carolyn Metzler '94, Christa Anderson '91, and Ellen Maycock '72. 

REU Spotlight: Clarkson University-SUNY Potsdam
Kazem Mahdavi

Students investigate Gaussian integers modulo n, knots and spatially embedded graphs, quantum algorithms, mixing in continuous quantum walks, and coloring properties of alternating knots with prime determinant.

Book Reviews
Mike Giannetto, Sarah Gourlie, & Rebecca Russ

Mike Giannetto reviews The Man Who Loved Only Numbers by Paul Hoffman. Sarah Gourlie reviews The Book of Numbers by John Conway and Richard Guy. Rebecca Russ reviews Duelling Idiots and Other Probability Puzzlers by Paul J. Nahin.

Fibonacci Decimals
Curtis D. Bennett

Infinite decimal calculus.  Is it a coincidence that 1/9899 = 0.0001010203050813213213455....?

The Fibonacci Association
Fredric T. Howard

Learn about the origins of this transcendental  international organization dedicated to Fibonacci numbers and related sequences.

Problem Section 
Andy Liu
Self-Referential Aptitude Test
Jim Propp

You will need your wits about you to solve this 20 question  multiple choice test that has the audacity to ask questions about its own answers.  If you want to start on a clean sheet, you can print off the questions. The answers are also available.