In another example of mathematical artistry, the designer(s) of Solomon’s Temple precinct used its most important distance to display the purpose of the entire project in mathematical terms.  They did this with the symbolic values of the numbers in a simple quasi- equation that also appears to have supplied the theme for Solomon’s dedication speech.

The two symbolically most important spots in the entire complex were clearly:

• the Ark of the Covenant which symbolized God’s presence on earth and stood centered in the 20 by 20 cubit Holy of Holies, and
   

• the 20 x 20 cubit outside Altar, centered on its elevated base before the Temple, open to the sky and connecting the precinct with God in heaven.  This is where the smoke rose from the sacrifices and where the fire fell from heaven to consume them.

These were the two locations that David specified when he saw the Angel of Pestilence beside the threshing floor on Mount Moriah, between earth and heaven (2 Samuel 24:16-25 and 1 Chronicles 21:16).  He built an Altar on that threshing floor, as instructed by his seer Gad, and then decreed in 1 Chronicles 22:1:

“This is to be the house of the Lord God, and this is to be an Altar of whole- offering for Israel”.

The Altar was already built, so the other place to which he pointed for the inner sanctum of the Temple was presumably the area where he had seen the Angel and which had thereby become so hallowed that it must have been included in the Holy of Holies.

The distance between the centers of these two core locations can be computed precisely from the Temple Court distances transmitted in the Rabbinic tractates Middot 2.1, 4.7, and 5.1, as discussed on the page about Temple dimensions. The layout drawing above reproduces the data from that tradition.

Despite the late date of these records from the first or second centuries CE, the archaeologist Leen Ritmeyer proposes that they most probably refer to the original design transmitted by priests and religious scholars because they roundly ignored the Hasmonean and Herodian additions and still listed the Temple Mount as square¹ although it had long been rectangular.

According to those transmitted dimensions, the distance between these two most important spots in the layout approximated a strikingly elegant quasi- equation between two of the constants we encountered in the mathematical creation story. 

There are only a few places in the number world where constants or their integer multiples intersect so closely with each other, and it seems likely that these nodes of encounter between the natural and the transzendental would have impressed ancient number mystics who appear to have attached symbolic and religious values to certain numbers.

The 36 pi side of this expression cumulates symbolic references to the sun and its cycles. We saw above that in Egypt, a circle formed the hieroglyph for the sun, the highest god there, and it was the main component in the Shen-Ring sign for “all that the sun circles” and “eternity”² .

The multiplier of 36 was also strongly associated with the circle. The Sumerians used a circle to write their numeral shar = 3,600 which marked a major step in their sexagesimal number system and was also the word for “circle”, “whole”, and “totality”³.  They probably also originated the division of the circle into 360 degrees, although our first surviving written record of that system is much younger.

The cultic year of their successors, the Assyrians, divided the yearly cycle into 360 days⁴, so it is most likely that the same division applied also to circles on earth.

The Egyptians also fit their twelve standard 30- day months into a 360- day civil calendar. They made up the difference with the actual solar year by inserting five extra days, birthdays of the gods that remained outside the flow of time, rather than spoil the purity of the more easily divided 360.

Their astronomers also divided a zodiac- like band of the sky into 36 regions which they used to tell time by the stars. These segments were called “decans” because their successive risings corresponded to the 36 Egyptian ten- day weeks.

The 13 C part of the quasi-equation matches the rest of the prayer with equal precision. Solomon turned around, blessed the assembly, and spread out his hands towards heaven to continue speaking to God, as recorded in 1 Kings 8:22-53, with a series of thirteen supplications for God’s compassion and mercy.

Although 13 is an unlucky number in modern Western folklore, and probably was one already in ancient Egypt, too, it had a much different connotation in ancient Israel.  It referred to the “Thirteen Attributes of Mercy” ascribed to God, as revealed to Moses on the mountain and listed in Exodus 34:6-7.

This number had great religious importance. The ritual tzitzit fringes of the Jewish tallit prayer shawl incorporate several allusions to it, and 13 is also the age for Bar and Bat Mitzvah⁷.

The thirteen invocations of God’s mercy in Solomon’s prayer appear thus to parallel these thirteen “Attributes of Mercy” and so to translate the thirteen- fold multiple of the sky number which the architects had carefully embedded in the place where Solomon stood.

As to that “sky” constant C in the crucial Ark- to- Altar distance, it was a natural fit for a prayer to heaven.  We find it with that meaning not only here and in the equations of the creation story, but the architects associated it also elsewhere with the sky. For instance,

• the east- west lengths of the Temple Court which were open to the sky added up to 87 cubit = 10 C.

• the open- to- the- sky widths on the south and north sides of the Porch were 17.5 cubit each which is just over 17.4 = 2 C;

• the inside length of the Sanctuary which represented heaven, and its distance from the centerline of the Mount, were both 61 cubits, or close to 60.9003 = 7 C.

This prominence of the sky- number in the appropriate areas of the layout, and the quasi- equation in the symbolically most important distance of the Temple precinct, suggest that Solomon simply pronounced in words what the designer of the Temple plan had expressed in that core distance. 

Moreover, Solomon's famous invocation in that prayer,

“Heaven itself, the highest heaven, cannot contain thee”,

matches the relationship between the two numbers involved since 13, the number of God’s mercy, is greater than 8.7, the number of heaven.  Actually, it is close to the numbers of heaven and earth and moon combined since  C + e + phi = 13.03635. 

Since Solomon had already named the sun separately in his first invocation, it appears thus that the quasi- equation for the core distance in his Temple, as well as his translation of it into the language of prayer, referred to the entire quartet of constants from the creation story.

Like Solomon’s two- part prayer, and like the above quasi- equation between whole multiples of pi and C, this precisely calculated line from Ark to Altar linked thus the sun and its repeating cycles with the symbols of God and sky and moon and earth.

In symbolic terms, this mathemagical link between the presences of God on earth, in the Holy of Holies, and in heaven, above the open- air Altar, amounts to a horizontal projection of the ladder to heaven that was believed to have risen from the Holy of Holies.

And the Temple designer(s) did not only allude to all that with this one ingeniously chosen core distance, but they also used fairly good values for both C and pi. 

The discrepancy of only 0.03034%  from the latter may have been due partly to the designers' need to work with whole cubits for most of the other distances.  However, even without any allowance for that possible constraint, their accuracy was at least in the same range as that computed by the much later Greek scientist Archimedes (about 287 to 212 BCE) who set the fences for this constant from 0.024% below to 0.040% above the actual value.

This is no reflection on Archimedes who probably had better things to do than to pursue a repetitive, mindless, and useless calculation once he had demonstrated the method, but it should lay to rest those persistent myths about Solomon's bad pi.