The Kaaba appears to express a geometrical progression of adjacent odd numbers starting with one and three. This differs from the super-particular ratios findable within the right triangles of astronomical time periods in the Megalithic, ratio pairs separated by only one rather than two. However, the multiple-square rectangles, used by the megalithic as approximations to celestial ratios, made use of the three-square rectangle. One of the earliest of these rectangles, this rectangle approximates two pairs of ratios: The eclipse year (346.62 days) to the solar year (365.2422 days) and the solar year to the thirteen lunar month year (384 days)

Figure 1 The three-square approximations in a triple series of astronomical periods. Note that the diagonals relative to the base are the result of having three squares in a rectangle then one high and three along - and two different. Two such rectangles geometrically sum (their angles) to give that of the (First Pythagorean) 3-4-5 triangle, 36.8 degrees.

If one adopts a square of 36 inches side length and projects outwards from the triple-square, one generates succeeding "odd couples" 3:5, 5:7, 7:9 and then 9:11 inside the walls and then 11:13 as the normalised plan for the Kaaba.

Figure 2 The geometrical progression of odd sided rectangles leading to the Kaaba wall plan.

This suggests that the design was to include the building within an implicit progression of odd-sided rectangles for reasons connected to the monuments orientation to astronomical time (lunar maximum standstill) and the facility of the triple-square "origin point" for the geometrical progression and of the triple time periods relating to the lunar nodes, in figure 1.

When the unit side length for this architectural grid is the plain yard of three (English) feet and 36 inches, then

• The inner perimeter is 9 x 2 + 11 x 2 = 40 yards, 120 feet and 1440 inches, 1,440 being the number of Adam.
• The outer perimeter is then 11x 2 + 13 x 2 = 48 yards, 144 feet, or 1,728 inches, 1728 being 12 cubed (one possible meaning for the Kaaba name) associated then with Arks and Ages in the ancient traditions.

The 11 by 13 rectangle is therefore the perfect scheme for expressing Adam, (whose temple the Kaaba was said to originally be) in relation to the head number (sans zeros) of Krita Yuga number 1,728,000.

Figure 3 Numerically symbolic perimeters of the Kaaba walls

Since the Kaaba was aligned to the 18.618 years (6800 days) of the nodal period, then in those 6800 days, there are 19.618 eclipse years (of 346.62 days). And this is exactly the ratio generated at the centre of the rectangular progression of figure 2 where the three-square rectangle has a diagonal that stands in the ratio of 19.618 to 18.618. If the three-long base of the rectangle is 18.618 years then the diagonal is 19.618 eclipse years long because such right triangles (half the rectangle) represent the inverse relationship of periodic frequency (within the same period) as well as the (same) ratio between periods.

Figure 4 The ratio between eclipse and solar years will be inversely reflected in the number of each contained in the 18.618 nodal period of the Moon's orbit.

This reveals that the eclipse and solar year lengths express a rationic difference normalised to a unit of time equal to 18.618 days. There are 18.618 of these in the eclipse year and 19.618 of these in the solar year, but what is this 18.618 day period? It is the time taken for the moon's node to move one DAY in angle on the ecliptic, and this is the average angle traversed by the sun on the ecliptic in one solar day. It is therefore true that the movement of the lunar nodes are synchronised to the sun's motion per day according to the number 18.618. The nodes are slower and retrograde in their angular motion and so the nodes take 18.618 solar years to completely traverse the ecliptic.

For the Kaaba, it is profoundly significant that the two numbers (1440 and 1728) naturally emerge from the three-square geometry which encapsulated the meaning of the monument's orientation; only when 36 units (inches) is taken as the unit length, and both sides of the rectangle are repeatedly lengthened by two units. Most ancient temples employed grid designs and most ancient mythology seems to have found a use for 1440 and 1728 in some of their greatest stories, but the Kaaba links, in an original and probably unique way, mythological numbers to astronomical facts in the numerical geometry of its design and its orientation of the Moon's Maximum Standstill.

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