Column

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 […]

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 […]

Math
Temple Circles
One tradition that flourished 200 years ago in Japan, during its period of isolation from the western world, involved Euclidean geometry. Scholars and others would inscribe geometric problems on wooden tablets, then hang the tablets under the eaves of Shinto shrines and Buddhist temples as offerings. Such a tablet is called a sangaku, which means […]

Math
Temple Circles
One tradition that flourished 200 years ago in Japan, during its period of isolation from the western world, involved Euclidean geometry. Scholars and others would inscribe geometric problems on wooden tablets, then hang the tablets under the eaves of Shinto shrines and Buddhist temples as offerings. Such a tablet is called a sangaku, which means […]

Math
Strange Orbits
Like toy cars chasing each other on a looped racetrack, three stars can, in principle, trace out a figureeight orbit in space. This newly discovered, mathematically surprising pattern of motion arises from the force of gravity acting on three bodies of equal mass. Their movements are timed so that each body in turn passes between […]

Math
Strange Orbits
Like toy cars chasing each other on a looped racetrack, three stars can, in principle, trace out a figureeight orbit in space. This newly discovered, mathematically surprising pattern of motion arises from the force of gravity acting on three bodies of equal mass. Their movements are timed so that each body in turn passes between […]

Math
Prized Geometric Logic
Computer programs can handle all sorts of data, from sums of money in bank accounts to sensor readings from scientific instruments. In many cases, the data are a set of discrete elements, such as temperatures. Moreover, some elements of a set may be larger in value than others, or they may exhibit some other relationship […]

Math
Buses on Quantum Schedules
Anyone who has waited for a bus in the city has probably casually observed that, after an inordinately long wait, two or three buses often come along at the same time. The question of why such bunching seems to happen has prompted all sorts of speculation. Some claim that bus bunching is actually a rare […]

Math
Subtle Logic, Winning Game
Seemingly simple games can serve as thoughtprovoking exercises in mathematical logic. They can provide deep insights into subtle issues that confront logicians who are interested in the foundations of mathematics. Socalled Ehrenfeucht games have proved particularly useful for tackling certain aspects of mathematical logic. They were developed in the 1960s by Andrzej Ehrenfeucht, who is […]

Math
Mayan Mars
The curiously looping movements of the planets relative to the stars have presented all sorts of puzzles to keen, patient observers of the night sky. In 1601, Johannes Kepler (15711630) undertook the challenge of deciphering the orbit of Mars and developing a mathematical theory of its motion to fit observations of the planet’s changing position […]