Math
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MathAppealing Numbers
The ancient Greeks, especially the Pythagoreans, were fascinated by whole numbers. They defined as “perfect” numbers those equal to the sum of their parts (or proper divisors, including 1). For example, 6 is the smallest perfect number-the sum of its three proper divisors: 1, 2, and 3. The next perfect number is 28, which is […]
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Math
Immersed in Klein Bottles
“Need a zero-volume bottle? Searching for a one-sided surface? Want the ultimate in nonorientability?” One way to depict a Klein bottle. Computer-generated image by John Sullivan, University of Illinois at Urbana-Champaign Joining the top and bottom of this rectangle produces a cylinder. Matching the arrows of the remaining two sides produces a Klein bottle. One […]
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Math
White Narcissus
The elegant, swooping forms carved out of wood by sculptor Robert Longhurst often resemble gracefully curved soap films that span twisted loops of wire dipped into soapy water. Alhough these abstract sculptures bear an uncanny resemblance to mathematical forms known as minimal surfaces, they emerge from Longhurst’s imagination rather than from mathematics. An original design […]
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Math
Fibonacci’s Chinese Calendar
In a book completed in the year 1202, mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes productive from the second month on? The total […]
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Math
Scheduling Random Walks
Juggling competing demands in a network of feverishly calculating computers drawing on the same memory resources is like trying to avert collisions among blindfolded, randomly zigzagging ice skaters. Example of a graph with one token poised to take a random walk. In this example of dependent percolation, a fickle demon would win (so far), but […]
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Math
Scheduling Random Walks
Juggling competing demands in a network of feverishly calculating computers drawing on the same memory resources is like trying to avert collisions among blindfolded, randomly zigzagging ice skaters. Example of a graph with one token poised to take a random walk. In this example of dependent percolation, a fickle demon would win (so far), but […]
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Math
Quirks of video poker
Even with perfect play over a long time, unfavorable odds and limits on how much a gambler may win per machine make playing video poker into a losing game.
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Math
Reassessing an ancient artifact
The famous Mesopotamian clay tablet known as Plimpton 322 represents an ordered list of worked examples that a teacher would use to prepare a sequence of closely related questions about squares and reciprocals for student exercises.
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Math
Scheduled random walks skirt collisions
Researchers in theoretical computer science have made progress in settling the question of whether a clairvoyant scheduler can regulate the timing of moves by random walkers on a grid to keep them from ever colliding.
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Math
Folding Maps
Anyone trying to refold an opened road map is wrestling with the same sort of challenges confronted by origami designers and sheet metal benders. The problem of returning a creased sheet to its neatly folded state gets tougher when you’re not sure if the sheet can be folded into a flat packet and when you’re […]
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Math
Folding Maps
Anyone trying to refold an opened road map is wrestling with the same sort of challenges confronted by origami designers and sheet metal benders. The problem of returning a creased sheet to its neatly folded state gets tougher when you’re not sure if the sheet can be folded into a flat packet and when you’re […]