All Stories by Ivars Peterson
- Math
Dangerous Problems
Some mathematical problems are easy to describe but turn out to be notoriously difficult to solve. Nonetheless, despite their reputed difficulty and repeated warnings from those who had failed to solve them in the past, these infamous problems continue to lure mathematicians into hours, days, and even years of futile labor. Billiard-ball trajectory after 15 […]
- Math
Dangerous Problems
Some mathematical problems are easy to describe but turn out to be notoriously difficult to solve. Nonetheless, despite their reputed difficulty and repeated warnings from those who had failed to solve them in the past, these infamous problems continue to lure mathematicians into hours, days, and even years of futile labor. In a presentation this […]
- Math
The Math Game
The television game show Who Wants to Be a Millionaire regularly attracts a huge audience. Can a mathematical game show hold its own against such competition–especially without lifelines, dramatic lighting effects, precarious chairs for contestants, and Regis Philbin as host? Probably not, but it can still be great fun. More than 200 mathematicians and students […]
- Math
Turn of the Screw
“What we are told about Archimedes is a mix of a few hard facts and many legends,” Sherman Stein of the University of California, Davis notes in his book Archimedes: What Did He Do Besides Cry Eureka? A three-bladed Archimedes screw. Courtesy of Chris Rorres. I was reminded of that statement when my son Kenneth […]
- Math
Conquering Catalan’s Conjecture
Innocent-looking problems involving whole numbers can stymie even the most astute mathematicians. As in the case of Fermats last theorem, centuries of effort may go into proving such tantalizing, deceptively simple conjectures in number theory. Now, Preda Mihailescu of the University of Paderborn in Germany finally may have the key to a venerable problem known […]
- Math
Algebra, Philosophy, and Fun
I don’t often encounter the words “philosophy” and “fun” right next to the term “algebra.” Nowadays, these words don’t seem to fit together comfortably. However, the three terms do appear in the title of an engaging little book called Philosophy and Fun of Algebra, written by Mary Everest Boole (1832–1916) and published in 1909. I […]
- Math
Squares, primes, and proofs
Mathematicians have proved the so-called local Langlands correspondence, a broad generalization of a surprising connection between prime numbers and perfect squares.
- Math
Losing to win
Two games of chance, each guaranteed to give a player a predominance of losses in the long term, can add up to a winning outcome if the player alternates between the two games.
- Math
Fractal Roots and Artful Math
The term “mathematical art” usually conjures up images of M.C. Escher’s endless staircases, Möbius-strip ants, and mind-boggling tilings. Or it might remind one of the intimate intertwining of mathematics and art during the Renaissance with the development of perspective painting and eye-teasing stagecraft. A view of the recent MathArt/ArtMath show at the Selby Gallery in […]
- Math
Fractal Roots and Artful Math
The term “mathematical art” usually conjures up images of M.C. Escher’s endless staircases, Möbius-strip ants, and mind-boggling tilings. Or it might remind one of the intimate intertwining of mathematics and art during the Renaissance with the development of perspective painting and eye-teasing stagecraft. A view of the recent MathArt/ArtMath show at the Selby Gallery in […]
- Math
Candy for Everyone
Several students are sitting in a circle. Each student has an even (though not necessarily the same) number of wrapped pieces of candy. On a signal, each student passes half of his or her trove to the student on his or her right. Between signals, the teacher (reaching into an inexhaustible goody bag) gives any […]
- Physics
Electrical superball pulls itself together
A strong electric field can drive tiny particles of a superconductor to bind themselves together into a remarkably sturdy ball.
