Sacred Number

Rectangles have a number of uses and, from the classical age until now, they have become the preferred floor plan for buildings. Numerically, we tend to see them as either a proportion or as an area.

As a proportion a rectangle can represent the ratio of the length to the width, as at,

1. Carnac, the Crucuno rectangle that embodies both two 3,4,5 triangles (the ratio of 3:4) or a rational version of Pi, in that case 25/8 (see previous post, ratio 32:25).
2. Stonehenge, the Station Stone rectangle that embodies two 12,13,5 triangles, ratio 12:5
   
3. Chartres, that manifests the nested ratios of one to the square root of three, the basis of the Gothic style, ratio 1:1.732, almost exactly 56:97.

As an area, a rectangle can embody a special number as the product of the two sides as at,

1. The Giza Pyramid in which the height times the south side can, in feet, yield a rectangle with an area the length of a degree of latitude (see Sacred Number, chapter 4).
2. The Parthenon that, as a rectangular Hekatompedon, has an area 100 times 100 or 10,000 square units (see Parthenon page)
   

In metrology, any reference length can also symbolise one of the key dimensions of the Earth itself according to the ancient model of the Earth, and so a rectangle's side can then divide into the Earth itself.

What is less known is that, in studying astronomical periods, a rectangle can help visualise the numerical interdivision of time periods such as those of the Moon, the solar year, Venus and so on. The same is true of triangles, which would have allowed ancient peoples to know, for example, the sidereal period of a planet from a knowledge of its synodic period, the latter being easily determined via counting on Earth.

To break out of this deadlock, I will (in the next weeks) present a series of examples, of "things that worked for me" to demonstrate that, simple as these techniques often are, the conclusions they lead to can often be extraordinary, bringing fresh insight to astronomy and ancient monumental architecture.

A very simple example involves the synodic period of Venus, a very important "star" in the ancient world, in fact a goddess and Aphrodite for the Greeks. In Matrix of Creation I discovered that the slight inexactitude of 8 solar years of 365.242 days equal to 5 Venus synods disappeared if the "practical year" of exactly 365 days was taken. 365 divides by five to yield a natural division of the year into five periods. (one calandar the Egyptians used was of 360 days plus five Neters. )

A very simple rectangle emerges with sides in this proportion, five by eight units of 73 days.

By looking at the two periods along the sides the way in which they both generate a common long period can be studied. Therefore, a rectangle can be used to analyse synchronicity of celestial time periods. Venus is the tidiest example of this but I will show that as an analytical tool the rectangle can show both the overall pattern of relationship and the building blocks out of which that relationship is built.

On the left is the "matrix" view  of the same Venus cycle. It demonstrates that there are two ways of multiplying 5 and 8 to get 40, and that these two ways (like the sides of the rectangle) are time periods belonging to Earth and Venus, whilst 73 days "belongs" to both as the common denominator.

 Another way of expressing 8 and 5 is as polygonal structures. Whilst today, the octagon is associated with Islamic architecture and perhaps from thence, as a norm of the Knights Templars, Charlemagne built the beautiful octagonal Palatine Chapel (lit. "Palace Chapel") when he became the first Holy Roman Emperor, three hundred years before the First Crusade.

One hundred years before this, the octagonal Dome of the Rock  had been built in Jerusalem. [The star at the focus of the crescent moon in the Islamic flag is Venus, a proximity that always occurs as the lunar crescent grows from the west.]

Whilst the U.S. military chose a Pentagon motif, this is only practical with larger buildings and the pentagonal star has instead become a powerful emblem and symbol of power or has to be incorporated within the golden rectangles of classical architecture.

The octagon is also a polygon most like a circle, and expresses balance of eight directions. Eight is (2² x 2) whilst Twelve, the basis of the Zodiac and classical geomancy, is (2² x 3), is useful for King Arthur's knights as a table and incorporates the square root of three within its geometries. Interestingly, within the octagon on the right there are the "knight's move"  of two units by one unit between every other corner, and this has the length of the square root of five, the same root behind the golden mean and pentagon. Five and Eight really are connected.