Ivars Peterson has made presentations at schools, colleges, professional meetings, banquets, and many other venues before diverse audiences, ranging from students and classroom teachers to NASA engineers and math enthusiasts.
Few people expect to encounter mathematics on a visit to an art gallery or even a walk down a city street (or across campus). When we explore the world around us with mathematics in mind, however, we see the many ways in which mathematics can manifest itself, in streetscapes, sculptures, paintings, architectural structures, and more. This illustrated presentation offers illuminating glimpses of mathematics, from Euclidean geometry and normal distributions to Riemann sums and Möbius strips, as seen in a variety of structures and artworks in Washington, D.C., Philadelphia, Toronto, Ottawa, Montreal, New Orleans, and many other locales. Bibliography.
The Jungles of Randomness
From slot machines and amusement park rides to dice games and shuffled cards, chance and chaos pervade everyday life. Sorting through the various meanings of randomness and distinguishing between what we can and cannot know with certainty proves to be no simple matter. Inside information on how slot machines work, the perils of believing random number generators, and the questionable fairness of dice, tossed coins, and shuffled cards illustrate how tricky randomness can be. Bibliography.
Newton's Clock: Chaos in the Solar System
With astronomical questions inspiring new mathematics, the remarkable insights of Johannes Kepler, Isaac Newton, and Henri Poincaré paved the way to celestial mechanics and modern notions of chaotic dynamics. The result is a new picture of a solar system less placid and predictable that its venerable clockwork image would suggest. Bibliography.
A Journey into Mathematical Art
From Fibonacci numbers and the digits of pi to tetrahedra, fractals, and Möbius strips, mathematics has inspired a wide variety of artists. Many people are familiar with the work of M. C. Escher and aware of the intertwining of math and art during the Renaissance, but the realm of mathematical art is far wider and more diverse than most people realize. An illustrated survey of contemporary math-related art illuminates these rich interactions. Bibliography.
Pancake Sorting, Prefix Reversals, and DNA Rearrangements
The seemingly simple problem of sorting a stack of differently sized pancakes has become a staple of theoretical computer science and led to insights into the evolution of species. First proposed in The American Mathematical Monthly, the problem attracted the attention of noted mathematicians and computer scientists. It now plays an important role in the realm of molecular biology for making sense of DNA rearrangements. Bibliography.
Since its discovery in the 19th century, the astonishing one-sided, one-edged Möbius strip has confounded and fascinated generations of people, inspiring stories, magic tricks, patents, artworks, cartoons, playground equipment, and much else. Learn more than you ever thought possible about how a mathematical object conquered the modern world. Bibliography.
Soap Bubbles in Math, Science, and Art
Artworks dating back to the invention of soap illustrate the wonder of soap bubbles and soap films. Soap bubbles have inspired not only art but also important developments in mathematics and science. Get a fresh perspective on minimal surfaces and their role in art, mathematics, science, and engineering. Bibliography.
Workshop: Writing Mathematics Well (1 or 2 hours)
The importance of communicating mathematics clearly and effectively is evident in the many ways in which mathematicians must write, whether to produce technical reports, expository articles, book reviews, essays, referee's reports, grant proposals, research papers, evaluations, or slides for oral presentations. With a focus on exposition, this workshop offers tips for improving writing skills, from grammar and usage to organization and manuscript or slide preparation. It also suggests how participants can contribute to the public understanding of mathematics. Bibliography.
Copyright © 2010 by Ivars Peterson