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 or other markings.Different species generally exhibit distinctive, recognizable patterns. Spot patterns are most common, but some species have stripes or a combination of spots and stripes. In every case, the patterns are symmetric. The position, size, and colo...

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 completes the course in the shortest time.Even in recreational orienteering, participants typically start off at staggered times. In that way, each person (or group) navigates the course individually and obtains no help from others on the course. In practice, however, competitors some...

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.The storyteller would clean and smooth the ground, then use his fingertips to press into the sand a rectangular grid of equidistant dots. As he talked, he would trace a winding line among the dots. More often than not, he would draw the line in one continuous motion to create a closed loop. A line could intersect itself but could not be traced...

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 you and, at other times, only a few vehicles in sight.From a physicist's point of view, traffic flow can be regarded as a "many-body system of strongly interacting bodies." Various studies have revealed that such systems can show wavelike behavior and abrupt transitions from one state...

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 you and, at other times, only a few vehicles in sight.From a physicist's point of view, traffic flow can be regarded as a "many-body system of strongly interacting bodies." Various studies have revealed that such systems can show wavelike behavior and abrupt transitions from one state...

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 any amateur to compose music without having to know the techniques or rules of composition. The London music publisher Welcker, for example, issued a "Tabular System whereby the Art of Composing Minuets is made so easy that any person, without the least Knowledge of Musick, may compose ten...

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 any amateur to compose music without having to know the techniques or rules of composition. The London music publisher Welcker, for example, issued a "Tabular System whereby the Art of Composing Minuets is made so easy that any person, without the least Knowledge of Musick, may compose ten...

The simple mathematical concept of a pursuit curve can serve as the starting point for creating wonderfully intricate artistic designs.Pursuit curves can arise in a variety of situations. Suppose, for instance, that four bugs are at the corners of a square. They start to crawl clockwise at a constant rate, each moving toward its neighbor. At any instant, they mark the corners of a square. As the bugs get closer to the original square's center, the new square they define rotates and diminishes in size. In reaching the center, each bug travels on a logarithmic spiral with a length equal to the s...

The simple mathematical concept of a pursuit curve can serve as the starting point for creating wonderfully intricate artistic designs.Pursuit curves can arise in a variety of situations. Suppose, for instance, that four bugs are at the corners of a square. They start to crawl clockwise at a constant rate, each moving toward its neighbor. At any instant, they mark the corners of a square. As the bugs get closer to the original square's center, the new square they define rotates and diminishes in size. In reaching the center, each bug travels on a logarithmic spiral with a length equal to the s...

The simple mathematical concept of a pursuit curve can serve as the starting point for creating wonderfully intricate artistic designs.Pursuit curves can arise in a variety of situations. Suppose, for instance, that four bugs are at the corners of a square. They start to crawl clockwise at a constant rate, each moving toward its neighbor. At any instant, they mark the corners of a square. As the bugs get closer to the original square's center, the new square they define rotates and diminishes in size. In reaching the center, each bug travels on a logarithmic spiral with a length equal to the s...