Are crop circles man-made or a genuine mystery. Here's some of the best evidence for a paranormal phenomenon.
Some researchers contend that certain crop circle formations contain sophisticated geometry that an ordinary hoaxer most likely would not even understand. Gerald S. Hawkins, former Chairman of the astronomy department at Boston University, says that he detected relationships between crop circles and Euclidean geometry. According to an article at "The Crop Circular", "Hawkins found that he could use the principles of Euclidean geometry to prove four theorems derived from the relationships among the areas depicted in crop circles. He also discovered a fifth, more general theorem, from which he could derive the other four. 'This theorem involves concentric circles which touch the sides of a triangle, and as the [triangle] changes shape, it generates the special crop-circle geometries,' he says. Hawkins could find no reference to such a theorem in the works of Euclid or in any other book that he consulted. In July 1995, however, 'the crop-circle makers... showed knowledge of this fifth theorem.'"
At least one article claims that the circle makers, whoever or whatever they are, have been encoding within crop circles diatonic ratios - how notes in music are related to each other. "Musicians have used the musical notes of the first octave to encode messages in their music," the article says. "For example, the last fugue of Bach keeps repeating notes B-A-C-H. The Circlemakers, since 1988, have also been encoding messages by including diatonic ratios, and hence sets of notes. When geometries are tested against lists of initials, the code appears to fit one and only one list: the first 25 presidents of the Society for Psychical Research of London." A reason why the circle makers might identify these people is not offered in the article. "Music and Harmonics" at Crop Circle Research.com offers additional information and some sound samples.
"The Sacred Geometry of Crop Circles" says that so-called sacred geometry is evident in crop formations and reflect "the universe, its pure forms and dynamic equilibriums shared a higher purpose: the attainment of spiritual wholeness through self-reflection, thereby giving structural insight into the workings of the inner self. When analyzing crop circle forms through the precise and unalterable practice of sacred geometry one cannot help but appreciate that a mind of scholarly intelligence is involved. That these symbols are occurring primarily in wheat, the very symbol of the Earth Mother, is significant in itself. Perhaps they are here to draw us as a race together by this interaction with our symbol of life?"