Math

Math
Art of Pursuit
The simple mathematical concept of a pursuit curve can serve as the starting point for creating wonderfully intricate artistic designs. Four “bugs” chasing one another produce an intriguing pattern of nested, rotated squares. Courtesy of John Sharp. Pursuit curves based on a starshaped polygon. Courtesy of John Sharp. Example of a pattern in which the […]

Math
Pursuing Pursuit Curves
A pursuit curve is the path an object takes when chasing another object. Such a path might result from a fox pursuing a rabbit or a missile seeking a moving target. This set of superimposed “snapshots” shows the lines of sight at regular intervals of four “bugs” chasing one another, all moving at the same […]

Math
Acoustic Residues
There’s a surprising mathematical ingredient in the sound of many performing artists and recording stars. It manifests itself in the form of clusters of panels hanging on the walls of recording studios, concert halls, nightclubs, and other venues. Sculpted from wooden strips separated by thin aluminum dividers, each panel consists of an array of wells […]

Math
Random Home Runs
For fans of majorleague baseball, one of the highlights of the current season is the rate at which Barry Bonds of the San Francisco Giants is hitting home runs. Through June 25, Bonds has hit 39 home runs in 77 games, already setting the record for the most home runs before the allstar break in […]

Math
Bubbles and Math Olympiads
Predicting the geometric shapes of soap bubble clusters can lead to surprisingly difficult mathematical problems. Which one of these two configurations of five planar bubbles of equal area has the smaller total perimeter? The more symmetric candidate isn’t always the winner. Frank Morgan Frank Morgan of Williams College in Williamstown, Mass., recently illustrated such difficulties […]

Math
Bubbles and Math Olympiads
Predicting the geometric shapes of soap bubble clusters can lead to surprisingly difficult mathematical problems. Which one of these two configurations of five planar bubbles of equal area has the smaller total perimeter? The more symmetric candidate isn’t always the winner. Frank Morgan Frank Morgan of Williams College in Williamstown, Mass., recently illustrated such difficulties […]

Math
Surprisingly Square
Mathematicians take a fresh look at expressing numbers as the sums of squares.

Math
Möbius Accordion
Artist Susan Happersett of Jersey City, N.J., has come up with a novel twist on the venerable Möbius strip: a playful, eyecatching creation she describes as a Möbius accordion. Happersett Accordion Susan Happersett Thirteen Original Colonies. Susan Happersett Happersett Accordion Susan Happersett A Möbius strip, or band, is the remarkable onesided surface that results from […]

Math
Prime Twins
Number theory offers a host of problems that are remarkably easy to state but fiendishly difficult to solve. Many of these questions and conjectures feature prime numbers–integers evenly divisible only by themselves and 1. For instance, primes often occur as pairs of consecutive odd integers: 3 and 5, 5 and 7, 11 and 13, 17 […]

Math
Cosmic Numerology
Like the ancient Pythagoreans, astronomer Johannes Kepler (1571–1630) found numbers fascinating. Imbued with the same conviction of a natural order that drove Pythagoras (c. 580–500 B.C.) and his followers to search for an underlying numerical harmony, Kepler maintained that the physical universe was laid out according to a mathematical design that was simple and accessible […]

Math
Cosmic Numerology
Like the ancient Pythagoreans, astronomer Johannes Kepler (1571–1630) found numbers fascinating. Imbued with the same conviction of a natural order that drove Pythagoras (c. 580–500 B.C.) and his followers to search for an underlying numerical harmony, Kepler maintained that the physical universe was laid out according to a mathematical design that was simple and accessible […]

Math
Lava Lamp Randomness
Sealed within a transparent, tapered, liquidfilled cylinder, illuminated colored globs slowly rise and fall. Meandering and deforming, their shapes and paths change unpredictably. Invented in 1963, a decorative fixture in many homes during the 1970s, and still in production, Lava Lite lamps are now the object of renewed curiosity. Indeed, researchers have come up with […]