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Story's by O.Frank

Diatonic Crop Circles

Much of the pubic has bought into the story that two elderly English men, Dave and Doug, made the Crop Circles; this however is nonsense. They claimed to have used a board to trample down the wheat, but when they did so in a demonstration, most of the wheat stalks were broken. In real Crop Circles, the stems are never broken and look as if they had grown bent over. In many of the more complex patterns the grain stalks are woven like a basket; creating different "shading" to the Crop Circle design. The number of crop circles has reached maybe 10,000 documented sightings today. Some crop circles are as big as 100,000 square feet and as long as three-quarters of a mile. According to Freddy Silva, a Crop Circle researcher, there have been witnesses to a Crop Circle formation. In 1972 a group of forty people on a hill, watching for the "Crop Circle makers," saw a large section of wheat, in the field below them, just "lie down in a spiral pattern as though a lady’s fan were opening." It was estimated that the complete incident took about fifteen seconds.

The most dramatic and interesting thing about Crop Circles is the precision of the Euclidean geometry they represent and what it may mean. Euclidean geometry is a type of math discovered by Euclid around 300 BC, and put in a three-volume book called Elements. In the February 1, 1992 weekly newsmagazine, Science News, Professor Gerald Hawkins, astronomer and mathematician, presented the results of his mathematical analysis of the Crop Circles. After studying hundreds of Crop Circles he found that not only was the geometry in the Crop Circle designs extremely precise, but they fall into four known Euclidean geometric theorems. He then discovered a fifth unknown theorem that describes the other four; a new general theorem, unknown to humans, that the other four are a sub-set of. But what is truly amazing is that the five theorems are diatonic ratios. Diatonic ratios govern the mathematical intervals that make up the notes in the western music scale. The Ancient Geeks called geometry "frozen music." So the Crop Circles are literally frozen music.

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copyright 2005 O.Frank