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- Math
Möbius and his Band
Making a Möbius strip. A Möbius band (or strip) is an intriguing surface with only one side and one edge. You can make one by joining the two ends of a long strip of paper after giving one end a 180-degree twist. An ant can crawl from any point on such a surface to any […]
- Math
Chemical Dissections
In recreational mathematics, a geometric dissection involves cutting a geometric figure into pieces that you can reassemble into another figure. For example, it’s possible to slice a square into four angular pieces that can be rearranged into an equilateral triangle. The same four pieces can be assembled into a square or an equilateral triangle. Sets […]
- Math
Super Bowls and Stock Markets
The Super Bowl “theory” links U.S. stock market performance to the results of the championship football game, held each January since 1967. It holds that if a team from the original National Football League wins the title, the stock market increases for the rest of the year, and if a team from the old American […]
- Math
A Perfect Collaboration
It seems an unlikely pairing. One was the most prominent mathematician of antiquity, best known for his treatise on geometry, the Elements. The other was the most prolific mathematician in history, the man whom his eighteenth-century contemporaries called “analysis incarnate.” Together, Euclid of Alexandria (c325–c265 BC) and Leonard Euler (1707–1783), born in Switzerland and at […]
- Math
Spinning to a Rolling Stop
Spin a coin on a tabletop. As it loses energy and tips toward the surface, the coin begins to roll on its rim, wobbling faster and faster and faster. Toward the end, the coin generates a characteristic rattling sound of rapidly increasing frequency until it suddenly stops with a distinctive shudder. Mathematician H. Keith Moffatt […]
- Math
A Remarkable Dearth of Primes
The pursuit of prime numbers–integers evenly divisible only by themselves and 1–can lead to all sorts of curious results and unexpected patterns. In some instances, you may even encounter a mysterious absence of primes. In 1960, Polish mathematician Waclaw Sierpinski (1882–1969) proved that there are infinitely many odd integers k such that k times 2n […]
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- Math
Lacing Shoes, Revisited
What is the best way to lace your shoes? This seemingly simple question, rooted in everyday life, can provoke passionate argument–and prompt a mathematical response. Three common lacing styles. Here are some alternative lacings you could try. The first two work only if your shoes have an even number of eyelet pairs. Watch out, though. […]
- Math
Lacing Shoes, Revisited
What is the best way to lace your shoes? This seemingly simple question, rooted in everyday life, can provoke passionate argument–and prompt a mathematical response. Three common lacing styles. Here are some alternative lacings you could try. The first two work only if your shoes have an even number of eyelet pairs. Watch out, though. […]
- Math
Punctured Polyhedra
A tetrahedron. Examples of unacceptable faces. A portion of an infinite lattice of interpenetrating tetrahedra. A tetrahedron has four triangular faces, four vertices, and six edges. Consider what happens when a vertex of one tetrahedron pierces the face of a second tetrahedron to form a new, more complicated polyhedron. In the resulting geometric form, one […]
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- Math
Five-Suit Decks, Traffic-Jam Puzzles, and Other Treats
Tired of playing the same old card games with the same old cards? One option is to expand the deck to include five suits instead of just four. To solve this difficult Rush Hour puzzle, you must move vehicles out of the way to permit the red car to exit at right. The best known […]
