# Radius or Diameter of a Circle Given Area

## r = sqrt(A/π); d = 2sqrt(A/π)

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Circles in the Cereal

Credit: Jabberocky
Source: http://commons.wikimedia.org/wiki/File:CropCircleW.jpg

In the course of a single night, someone transforms a field of grain into a geometric masterpiece. Elaborate circles bend the wheat in careful arcs. Yet, there's no sign of human interference. The crop circles of England attract tourists, scientists, and UFO researchers. Who makes these elaborate circles in the cereal?

#### Hoaxes and Artists

When the crop circles first appeared in the 1960s and 1970s, many people believed they were the work of aliens, psychics, or strange natural forces. When a new crop circle appears, visitors flock to the site. Farmers sell tickets. Helicopters and planes fly overhead to take pictures from above. In many ways, the crop circles are a British version of the American corn maze. These large-scale patterns are best seen from above but also fascinate walkers on the ground.

In the 1990s, the origins of the crop circles became public. Groups of artists had created these elaborate hoaxes to mock stories of UFO sightings. Each crop circle requires an enormous amount of planning. A good crop circle is both complicated and mysterious. Modern crop circle creators use computer-drafting software to help plan their designs. Then they put together a team. They set out to create the circles in a single night, using only ropes and boards to flatten the grain into intricate patterns. They work silently, in the dark, and before dawn, they melt away into the fields, leaving no traces of their involvement.

Credit: Ian Burt
Source: http://www.flickr.com/photos/28648431@N00/216172506

The designs of crop circles are getting increasingly elaborate. The designers create numerical puzzles based on Euclidean geometry or ancient artworks. They make fractals and even corporate logos. Some of the most talented crop circle artists actually travel the world, earning a living from their work.

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