Column
- Math
Dots and Boxes
The familiar pencil-and-paper game of Dots-and-Boxes sounds exceedingly simple. Given a square or rectangular array of dots, two players take turns joining two adjacent dots with a horizontal or vertical line. When such a move adds the fourth side of a box, the player who did the deed claims the box (marking it with his […]
- Math
Fractured Granite and Fractal Prints
A rectangular slab of polished granite gives an impression of solidity and permanence. With its straight lines and glossy surface, it’s an elegant, humanmade artifact meant to stand as a timeless monument or serve as an impermeable skin for a sleek skyscraper. A fractal stone print. Nat Friedman A two-sided fractal stone print by Nat […]
- Math
Crediting Basketball’s Three-Pointers
The adoption of the three-point field goal in basketball changed the game. Initially, its impact was limited, but in recent years, shooting three-point baskets has had a significant effect on game strategy and outcome. Many sports fans can’t resist the lure of quantifying performance–ranking teams, rating players, and keeping various statistics. Now, statistician Thomas P. […]
- Math
Chomping to Win
Even the simplest of games can pose tough mathematical challenges. One such game is Chomp. It was invented in the early 1970s by David Gale of the University of California, Berkeley, who was also responsible for the board game Bridg-it, and it was later dubbed Chomp by Martin Gardner. Chomp on a 5-by-6 field. The […]
- Math
Disorder in the Deck
Card players sometimes get lazy, shuffling a deck fewer times than necessary to randomize the cards. Indeed, persistently sloppy shuffling can have a significant impact on play–an effect that experts (and gamblers) can exploit to their advantage. However, the problem lay not in the computer but with human expectations. Subsequent research showed that hands in […]
- Math
Disorder in the Deck
Card players sometimes get lazy, shuffling a deck fewer times than necessary to randomize the cards. Indeed, persistently sloppy shuffling can have a significant impact on play–an effect that experts (and gamblers) can exploit to their advantage. However, the problem lay not in the computer but with human expectations. Subsequent research showed that hands in […]
- Math
Staying in Step
Late in the winter of 1665, an ailing Christiaan Huygens (1629–1695) was confined to his room for a few days. The Dutch physicist whiled away the hours of his confinement by closely observing and pondering the odd behavior of two pendulum clocks he had recently constructed. Huygens had obtained a patent on the first pendulum […]
- Math
Planes of Budapest
Nearly every Sunday during the winter of 1933 in Budapest, a small group of students would meet somewhere in the city at a park or cafe to discuss mathematics. The gathering typically included Paul Erdös (1913–1996), who was attending the University of Budapest, György (George) Szekeres, a recent chemical engineering graduate of the Technical University […]
- Math
Plato’s Molecule
In his dialogue Timaeus, the Greek philosopher Plato (427–347 B.C.) carefully laid out his reasoning for ascribing certain geometric shapes to the minuscule particles that constituted the four elements of matter. In his view, these elements–fire, air, water, and earth–were all aggregates of tiny solids, each one having the shape of one of the regular […]
- Math
Plato’s Molecule
In his dialogue Timaeus, the Greek philosopher Plato (427–347 B.C.) carefully laid out his reasoning for ascribing certain geometric shapes to the minuscule particles that constituted the four elements of matter. In his view, these elements–fire, air, water, and earth–were all aggregates of tiny solids, each one having the shape of one of the regular […]
- Math
Defending the Roman Empire
Years ago, when I was in high school and college, the board games Risk and Diplomacy served as wonderful playing fields where I could develop and exercise my tactical and negotiating skills. One issue that often came up in my forays into international intrigue was how to deploy my limited forces to defend far-flung territories […]
- Math
Möbius at Fermilab
Fermilab’s Wilson Hall. Courtesy of Fermilab. Soaring into the sky like a medieval cathedral, the twin towers of the structure known as Wilson Hall dominate the flat countryside surrounding the Fermi National Accelerator Laboratory (Fermilab) in Batavia, Ill. Named for physicist and accelerator builder Robert Rathbun Wilson (1914-2000), the building celebrates Wilson’s vision and skill, […]
