Math Trek
- Math
Turtle Tracks
One way to describe a geometric figure is in terms of the path generated by a moving point. Instead of defining a square, for example, as a four-sided polygon with equal sides and angles, you can call it the path generated by the following rule: Go straight for a distance s, turn 90 degrees right, […]
- Math
Cracking Fermat Numbers
Fermat numbers have what mathematicians sometimes describe as a “beautiful mathematical form,” involving powers of 2. They were of interest 400 years ago and are now the subject of a wide-ranging worldwide computer search. A Fermat number has the form 22n + 1, where n is a whole number equal to or greater than 0. […]
- Math
The Tangled Task of Distinguishing Knots
Consider the plight of a gardener struggling with a recalcitrant tangle of garden hose. Sometimes, no amount of pulling or twisting unsnarls the coils. At other times, the tangles readily come apart, and the hose emerges unknotted. Trefoil knot. Different views of the figure-eight knot. Robert Scharein Braid (left) and its closed form (right). Robert […]
- Math
Pinpointing Prey
Eight command neurons (black) represent the eight directions of the legs from which they receive input. Partner neurons (gray) send inhibitory signals. van Hemmen et al./Physical Review Letters Under cover of darkness, a burrowing cockroach skitters across the desert sand. Its rapidly moving legs excite tiny ripples that travel along the ground, tipping off a […]
- Math
A Graceful Sculpture’s Showy Snow Crash
Brent Collins has spent more than two decades carving gracefully curvaceous sculptures out of wood. Born of his imagination, rendered in wire and wax, then painstakingly realized in wood in his Gower, Missouri, workshop, each creation demands many weeks of labor. Whirled White Web: An award-winning, ill-fated snow sculpture. Séquin Central portion of Scherk’s second […]
- Math
A Graceful Sculpture’s Showy Snow Crash
Brent Collins has spent more than two decades carving gracefully curvaceous sculptures out of wood. Born of his imagination, rendered in wire and wax, then painstakingly realized in wood in his Gower, Missouri, workshop, each creation demands many weeks of labor. Whirled White Web: An award-winning, ill-fated snow sculpture. Séquin Central portion of Scherk’s second […]
- Math
Sliding-Coin Puzzles
Geometric arrangements of coins can serve as the basis for all sorts of puzzles. One popular variant involves going from one configuration to another by sliding coins, subject to given constraints, and doing so in the fewest possible moves. Rearrange the rhombus into a circle using three moves. Turn the triangle upside-down in three moves. […]
- 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 […]
