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Geometric Mysteries

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Intricate Patterns

Examining The Crop Circle Phenomenon


By James Donahue

November 2005


Everybody knows about Crop Circles. But nobody agrees on just who or what is making them, and why they exist for brief times in grain fields all over the world.


Often showing intricate geometrical and sometimes occult patterns that are so complex and perfectly patterned, the designs are best seen from the air and suggest hours of labor sometimes accomplished within brief time periods while no one is looking.


That they usually occur under cover of darkness makes the mystery even more astounding. If accomplished by human hand, as many would argue, the abilities of such pranksters to create such profound art without the help of lamps and measuring devices, including a surveyor’s sextant, leaves the observers confounded.


There appears to be two primary theories as to the origin of these spectacular artworks that come and go with each growing season. Some say they are an emerging art form; a contemporary graffiti that one writer in National Geographic suggests “will be written about in future art history books as the most remarkable artistic innovation to emerge from the Twentieth Century.”


The second theory is that they are mysterious messages from extraterrestrials, created by unknown technology from alien craft passing overhead in the night sky. One thought is that because of their brief existence, the circles might be markers for time travelers, giving exact dates in which to land.


Whether they existed prior to the first stories about them in southern England in the mid-1970s is not known. The first media records of designs in grain fields showed relatively simple formations appearing overnight in the area already known as home for some of the strangest Neolithic sites in the world including Stonehenge, Avebury and Silbury Hill. In every case the crops are flattened and the stalks bent, but not broken.


The phenomenon seemed to gain momentum after the initial stories were told. Now the formations are showing up in fields in Australia, South Africa, The United States, Russia, and China. They are just about anywhere that farmers grow crops and that the field can be altered so that an image is clearly visible from the air.


And each year, the centerpiece of the circle art appears to continue to be in the fields of southern England, where more than 100 formations appear each season.


While simplistic at first, the designs have been growing in complexity until they are getting downright sensational in their appearance. Sometimes it seems sad to realize that their existence can only last but a few days until nature returns to normal or until the crop is harvested.


The UFO theories were set back in 1991 when Doug Bower and Dave Chorley claimed responsibility for the crop circles in England. Bower was found to have a group of people known as the Circlemakers, who designed their mischief before stealing off in the night to create yet a new and more intricate design.


Supporters of the human manufacturing theory suggest that many groups like that of Bower and Chorley must exist all over the world, all doing their covert work in the dead of night.


On the other side of the coin, the study of the circles by dedicated UFO-believers, has become a science in itself. The students have evolved into a thriving cottage industry of sightings, measurements, speculations and publications. The serious enthusiasts call themselves cereologists, taking the name of Ceres, the Roman goddess of agriculture.


The first deformations appeared as simple, nearly perfect circles of grain flattened in a spiral pattern. But as the years have passed, the patterns now consist of circles in groups, circles inside rings or circles with spurs and other appendages.


Retired astronomer Gerald S. Hawkins has noted something interesting about the designs that could only be appreciated by dedicated mathematicians. He notes that a number of ingenious and previously unknown geometric theorems are showing up in what he calls “artwork in the crops.”


Using data from published ground surveys and aerial photographs, Hawkins measured the dimensions and calculated the ratios of the diameters and other key features in 18 different patterns that included more than one circle or ring.


In 11 of the patterns, Hawkins found ratios of small whole numbers that precisely matched the ratios defining the diatonic scale. These ratios produce the eight notes of an octave in the musical scale corresponding to the white keys on a piano.


The discovery prompted Hawkins to look for and find geometric relationships among the circles, rings and lines of other distinctive patterns.


His first theorem was found in a triplet of crop circles found in 1988. He noticed he could draw three straight lines, or tangents, that touched all three circles. By drawing in the equilateral triangle formed by the circles’ centers and adding a large circle centered on this triangle, he proved the theorem that reads: “The radio of the diameter of the triangle’s circumscribed circle to the diameter of the circles at each corner is 4:3.”


Since that discovery, Hawkins claims three more geometric theorems, all involving diatonic ratios arising from the radios of areas of circles among crop-circle patterns.


Amazingly, Hawkins could find none of the theorems in the works of Euclid, the famed Greek geometer who established the basic techniques and rules for Euclidean geometry. He also failed to find the crop-circle theorems in any of the mathematics textbooks and references that he consulted.


Thus Hawkins appears to have proved that either the artists are amazingly skilled in creative geometry or that the circles he examined were the creations of beings from out of this world.


In conclusion, all that this writer can say about crop circles it that they remain a true enigma of our time.

Field Graffiti?

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