Crop Circle Geometry
The oddity that follows has been known for some time...but is being reported just in case you missed it. Perhaps it proves that aliens know hidden connections between music and Euclidean geometry.
Crop circles involving inscribed polygons have been appearing in England since the 1970s, often in sizes up to 200 meters in diameter. One oddity is found in crop circle diagrams but can easily be expressed in mathematical terms.
Place a triangle "in" four concentric circles with its three sides tangent to the three inner circles and its three vertices on the outer circle:
Then, as the circle changes its shape, the respective areas of the circles make the ratios of the musical intervals, doremi etc.
Odd enough for you? If you want more, please consult the references below or one of these web sites: Sacred Crop Circle Geometry, Internal Geometry of Crop Circles, or Crop Circle Music.
Source: "Geometry in English Wheat Fields," Math Teacher, Dec. 1995 (p. 802) & 1998 (p. 441)
