Math Trek
- 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 […]
- Math
Fold-and-Cut Magic
One of the treats of holidays long past was an activity that involved folding, then cutting a sheet or strip of paper to reveal a lacy snowflake or a chain of identical spruce trees, connected at their sides so it looked like branches brushing up against each other. The result was invariably a delightful surprise. […]
- Math
Puzzling Lines
Sol LeWitt’s “Four-Sided Pyramid” at the National Gallery of Art’s Sculpture Garden in Washington, D.C. I. Peterson LeWitt’s “Wall Drawing No. 623” at the National Gallery of Canada in Ottawa, Ontario. I. Peterson Born in Hartford, Conn., in 1928, artist Sol LeWitt has often featured geometric and combinatorial themes in his numerous creations. His frequent […]
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- Math
Ancient Infinities
An ancient manuscript long hidden from public view has provided significant, new insights into the way Archimedes (287–212 B.C.) did his mathematical work more than 2,000 years ago. The manuscript, known as the Archimedes Palimpsest, is the only source of Archimedes’ treatise on the “Method of Mechanical Theorems.” As the oldest surviving Archimedes manuscript, it’s […]
- Math
Card Shuffling Shenanigans
Shuffling cards is a tricky business. It’s also a lucrative one for gambling casinos. In a game such as blackjack, an astute player can try to memorize the cards already played to have a better chance of predicting which cards will come up later, thus potentially gaining an advantage over the dealer and the casino. […]
