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## Is Sound Creating Crop Circles? (cont.)By Freddy Silva

In the February 1992 edition of Science News, Prof. Gerald Hawkins used the principles of Euclidean geometry to prove that four theorems can be derived from the relationships of elements in crop circles. More significantly, he discovered a previously unknown fifth theorem from which he could derive the other four. Despite an open challenge to over half a million subscribers none have been able to create such a theorem, which Euclid himself only hinted at twenty-three centuries earlier in his thirteen treatises on mathematics. So it came as a slight shock when its equilateral version materialized as a 160,000 sq. ft. crop circle at Litchfield, Hampshire, in 1995.

Since the crop circle theorems also produce diatonic ratios, a link exists between crop circles and musical notes, which are the by-product of the harmonic laws of sound frequency. Soon after, crop circles bearing unmistakable associations with sound began to appear. One contained a curious ratchet feature from which is constructed a musical diagram also dating to the Egyptians, the Lambdoma. Also known as the Pythagorean Table, it defines the exact relationships between musical harmonics and mathematical ratios.

But it was a convincing crop circle etched in barley at Goodwood Clatford­— which had its plants bent six inches from the top— that gave the proverbial nod to sound, for here was a representation of a cymatic pattern.

Cymatics is the study of vibrational wave patterns. One of its twentieth-century pupils was Swiss scientist Hans Jenny who painstaking captured on film the transmission of sound as it interacted with powders and liquids.

He observed how sound vibration created geometric shapes: a low frequency produced a simple circle encompassed by rings, whereas a higher frequency increased the number of concentric rings around a central circle. As the frequencies rose so, too, did the complexity of shapes, to the point where tetrahedrons, mandalas and other sacred geometric forms could be discerned. Like the Egyptians, Jenny enabled humanity to observe 'frozen music'.