# Column

1. Math

### Absolutely Abnormal

Identifying the normal (or even the abnormal) in mathematics can pose serious difficulties. In 1909, mathematician Émile Borel (1871–1956) introduced the concept of normality as one way to characterize the resemblance between the digits of a mathematical constant such as pi (the ratio of a circle’s circumference to its diameter) and a sequence of random […]

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2. Math

### Tolstoy’s Calculus

“Absolute continuity of motion is not comprehensible to the human mind. Laws of motion of any kind become comprehensible to man only when he examines arbitrarily selected elements of that motion; but at the same time, a large proportion of human error comes from the arbitrary division of continuous motion into discontinuous elements.” This striking […]

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3. Math

### Firm Data

Business firms range in size from boutiques operated by individuals to huge multinational corporations employing thousands. You would expect that there are fewer large businesses than small ones. In economics, however, it’s useful to characterize the size distribution of firms more precisely than that. Within an industry, for example, the firm size distribution would indicate […]

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4. Math

Ladybugs are among the most familiar of beetles. More than 4,000 species are found throughout the world, ranging in size from 4 to 18 millimeters. Also known as lady beetles or ladybirds, these insects (coccinellids) have rounded bodies and bright red, orange, or yellow wing covers, which usually bear an array of contrasting black spots […]

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5. Math

Ladybugs are among the most familiar of beetles. More than 4,000 species are found throughout the world, ranging in size from 4 to 18 millimeters. Also known as lady beetles or ladybirds, these insects (coccinellids) have rounded bodies and bright red, orange, or yellow wing covers, which usually bear an array of contrasting black spots […]

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6. Math

In the sport of orienteering, a competitor uses a detailed map (and perhaps a compass) to navigate his or her way across varied terrain following a course drawn on the map. Selecting the best available route, each participant races from one marker to the next in the required sequence. The winner is the person who […]

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7. Math

### Sand Drawings and Mirror Curves

To accompany the telling of a story or recounting of a fable, men of the Chokwe people in south-central Africa traditionally made sand drawings, called sona, to illustrate the tale. These highly stylized geometric illustrations also served as memory aids. Sand drawing. Paulus Gerdes Plaited mat designs. Mark Schlatter Lion’s stomach design. Mark Schlatter Example […]

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8. Math

### Waves of Congestion

You’re confined to a single lane as you drive along a narrow, winding road. The car in front of you suddenly slows, then just as inexplicably accelerates a short time later, only to slow again. As you keep adjusting to the leading car’s erratic speed changes, you sometimes find a clump of vehicles closely tailing […]

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9. Math

### Waves of Congestion

You’re confined to a single lane as you drive along a narrow, winding road. The car in front of you suddenly slows, then just as inexplicably accelerates a short time later, only to slow again. As you keep adjusting to the leading car’s erratic speed changes, you sometimes find a clump of vehicles closely tailing […]

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10. Math

### Mozart’s Melody Machine

Music publishing was a thriving trade during the latter part of the 18th century in Europe. Publishers vied with one another to print the works of the latest “hot” composer. Many of them looked for novel ways to entice new customers into their music shops. One such ploy was to publish systems that would allow […]

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11. Math

### Mozart’s Melody Machine

Music publishing was a thriving trade during the latter part of the 18th century in Europe. Publishers vied with one another to print the works of the latest “hot” composer. Many of them looked for novel ways to entice new customers into their music shops. One such ploy was to publish systems that would allow […]

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12. Math

### Art of Pursuit

The simple mathematical concept of a pursuit curve can serve as the starting point for creating wonderfully intricate artistic designs. Four “bugs” chasing one another produce an intriguing pattern of nested, rotated squares. Courtesy of John Sharp. Pursuit curves based on a star-shaped polygon. Courtesy of John Sharp. Example of a pattern in which the […]

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