Foundational Role of The Wisdom Schools

FOUR EUCLIDEAN THEOREMS AND NEW THEOREM

IN CROP CIRCLES DISCOVERED BY GERALD HAWKINS
See Diatonic Scales

Theorem 1

The ratio of the diameter of the triangle's circumscribed circle to the diameter of the circles at each corner is 4:3.

Theorem 2

For an equilateral triangle, the ratio of the areas of the circumscribed and inscribed circles is 4:1. The area of the ring between the circles (the annulus) is 3 times the area of the inscribed circle.

Theorem 3

For a square, the ratio of the areas of the circumscribed and inscribed circles is 2:1. If a second square is inscribed within the inscribed circle of the first, and so on (nth) then the ratio of the areas of the original circumscribed circle and the innermost circle is 2-to-the-n:1.

Theorem 4

For a regular hexagon, the ratio of the areas of its circumscribed and inscribed circle is 4:3.

Theorem 5 - New

As the triangle changes shape the circles expand and contract to touch the sides, and the diagram generates the four crop circle theorems.

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