GEOMETRIC THEOREMS Definitions A Crop geometry is an unembellished diagram with rotational symmetry, which contains a theorem that can be proved by Euclidean logic and constructions, and generally leads to a pair or more of diatonic ratios. A crop mandala is a pattern with rotational symmetry containing crop circle geometries which give diatonic ratios. Usually the mandala is embellished. For satellite and spaced circles, the diatonic ratio is large diameter divided by small diameter (above). For concentric circles, the diatonic ratio is area of outer circle divided by area of inner circle (above). For ringed circles, the diatonic ratio is given by the circle at the "up" edge of the ring, measured outward from the center of the formation.

