# Math

1. Math

### Appealing 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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2. 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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3. 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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4. 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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5. 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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6. 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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7. 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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8. 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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9. 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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10. 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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11. 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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