![]() Photo courtesy www.circlemakers.org Formation at Ogbourne St. George in Wiltshire |
The stalks inside a crop circle are typically bent into what is known as a swirl pattern, and the circles may spin clockwise or counterclockwise. In patterns with several circles, one circle may spin clockwise and another counterclockwise. Even a single circle may contain two "layers" of stalks, each spinning in a different direction.
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![]() Photo courtesy www.circlemakers.org A crop circle near Silbury Hill in Wiltshire, England, that resembles an Aztec Sun Stone |
![]() Photo courtesy www.circlemakers.org A formation at West Kennett in Wiltshire that looks like a Celtic symbol called the Triskell |
Some of the more sophisticated patterns are based on mathematical equations. Astronomer and former Boston University professor Gerald S. Hawkins studied several crop circles and found that the positions of the circles, triangles and other shapes were placed based on specific numerical relationships. In one crop circle that had an outer and an inner circle, the area of the outer circle was exactly four times that of the inner circle. The specific placement of the shapes indicates that, whoever the circlemakers are, they have an intricate knowledge of Euclidean geometry (the geometry of a flat surface introduced by the mathematician Euclid of Alexandria).
Some circles have thin lines leading away from them. These lines, called spurs, are not actually a part of the circle. They are created by the farmer's tractor.
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