Follow the construction process here.

Using geometry to find a square with a perimeter that is equal to the circumference of a circle is an ancient problem.  It is something of a litmus test for geometers to attempt new solutions.  Frank has discovered a new way to square the circle that unfolds from the sacred geometric form of the Vesica Piscis, a special intersecting of two circles. His method uses only a straight-edge and compass, with no measurements needed, and is the first to work from the inside out using the Vesica Piscis form.  The mathematics of Frank’s construction are known, and agree to within 99.9+% accuracy (between the measurements of the square and circle).

Within the discipline of sacred geometry, it is well known that when a circle is squared, the relationship between the relative sizes of the Moon and the Earth is made explicit. If the Earth is scaled to fit exactly within the perimeter of the square, then a circle of the same perimeter as the square will pass through the center of the Moon, if it were to touch the Earth.

However, Frank’s construction method is unique, because it not only yields the Earth-Moon relationship, but also delves inside the Earth, revealing a more subtle relationship between the size of the Moon and the size of the interior of the Earth.

The Earth has both an inner and outer core; together they form a sphere 6972 km in diameter. The Moon has a diameter of 3474 km, which is almost exactly half that of the Earth’s core (~99.7% agreement). In other words, two Moons, side by side fit exactly into the Earth’s core. Frank’s method yields points (noted by small white circles on the drawing on p. 40) that mark the relative size of the Earth’s core, and thus its relationship to the Moon.