When the disk of the Moon is also enclosed in a square, the first such coincidence is the appearance of Pythagorean {3-4-5} triangles in the geometrical construction resulting from its juxtaposition with the disk of the Earth.

Figure 3-21. Earth, Moon And {3-4-5} Triangles

Extending the construction to form a cross-section of the Grand Pyramid, the lengths of the component lines must be multiplied up, in this case by 12 (the sum of 3, 4 and 5), in order to continue expressing them all as whole numbers. This gives a unit exactly equal to 60 English miles, 60 being the product of 3, 4 and 5. Put another way, if the modulus of the diagram shown in Figure 3-22, equal to 1/132nd of the diameter of the Terrestrial reference sphere, the Grand span, is subdivided by the product of 3, 4 and 5 then the result is a unit of length which is exactly equal to a modern English or U.S. mile.

Figure 3-22. Earth, Moon And Grand Pyramid

In terms of the Grand span derived in Figure 3-22, the combined diameters of the Terrestrial and Lunar reference spheres is 168. That is also the number of hours in each and every week. Just as the Grand span is exactly divisible into 60 English miles, so the hour is divided into 60 minutes and the number of minutes in every seven-day period is exactly 10,080. Seven days is very roughly the period of a single Lunar quarter.

Figure 3-23. The Seven Days of The World

The radius of the large circle whose circumference is equal to the perimeter of the square around the Earth, taking π (pi) to be ²²/₇, is 5,040 miles. 5,040 is the product of all the numbers from 1 to 7, written 7! and is known as the factorial of seven.

5,040 = 1 × 2 × 3 × 4 × 5 × 6 × 7 = 7!

The modulus of the diagram shown in Figure 3-21 is 720 miles. 720 is the factorial of six.

720 = 1 × 2 × 3 × 4 × 5 × 6 = 6!

The circumference of the large circle, again taking π = ²²/₇, is exactly 528 Grand spans, or 31,680 miles, and this is of course equal in length to the perimeter of the square around the Earth, the base of the virtual cosmic Horizon Pyramid whose height is equal to the combined radii of Earth and Moon, or 5,040 miles.

Figure 3-24. Abhisambodhi Vairocana Mandala (Tibet, 14th Century)