Crop Circle Symbology
While the earliest crop circles manifested themselves in simple round patterns, they have increasingly over the last two decades developed vast and complicated geometric 
patterns. Researchers having delved into the mathematical symmetries of these designs and discovered complex rational formulae.
Three centuries B.C.E. the mathematical scholar Euclid devised four primary geometrical theorems on which he hinted there could possibly be a fifth theorem derived from. Twenty three hundred years later this fifth geometrical theorem was mysteriously exhibited in a one hundred sixty thousand square foot pattern of flattened, woven barley outside Litchfield, Hampshire in England. The astronomer Gerald S. Hawkins, former Chairman of the Boston University Department of Astronomy, has written exhaustively on this phenomena. *
Another intriguing facet of this complex geometry is its correlation to the diatonic ratio which is used to create the scale of musical notes. The mathematical interplay of the 
various triangles and circles woven into these crop circles demonstrate a fine understanding and pictorial example of this concept of the underlying nature of sound in a physical pictogram of the face of the earth.
This “frozen” music has echoes within many of the world’s religions. From the “sound” spoken by the Judeo-Christian God to create the universe. You can see such designs carved into the architectural stones of Gothic cathedrals. The Navajo and Hopi shamans are known to utter a “sound” to vibrate through the sand of their medicine paintings thus creating geometric patterns. These shamanistic vibration-created designs mirror the function and look of the Hindu mandalas which are purported to be the expressions of the word of the gods. It could also be why Islam uses geometrical designs to express their image of God. A large number of the “circles” that appear in England feature Celtic knots, crosses and other design work.
From the early religious concepts, man has considered the sun a representation of their “god”. This circle pattern was the simple design of the early crop circles. As these 
mysterious patterns developed, the “barbell” pattern of two circles connected by a straight line began to show up. Around one circle of many of these designs, extra patterns started taking form, mirroring the “holy” signs and symbols of a multitude of both aboriginal and established religious icons.
Now, the mystery of who is creating these crop circles has not been solved by any means. While there are those who say they are divinely created, others feel that there is an extraterrestrial source. According to the ancient Sumerians, the “gods” were beings who came from another planet. The truth could be some combination of the two seemingly diverse ideas. But if these are messages from “the gods”, then what are they trying to communicate and why are they using such elaborately mysterious methods to do so?
Written by Wm. Douglas Mefford
= = = = = = =
* NOTE: The circlemakers’ fifth theorem has been published in “The Mathematics Teacher”, the magazine of the National Council of Teachers of Mathematics. It may be obtained through your local library or ordered by e-mail. Attention “Kay Reuter/Customer Service Dept” orders @ nctm.org (remove spaces) Request information on ordering page 441, volume 91, Number 5. It is the May, 1998 issue of the magazine.
