Genesis 1:1 as a Tessellated Trefoil

This page introduces another symmetrical view of Genesis 1:1 that, like those introduced earlier, arises from a simple regular division of the words of the verse.

First, here is a reminder of the Bible's opening Hebrew words with their numerical implications:

There are 7 words comprising a total of 28 letters. Since c200 BC each letter has also functioned as a numeral. The values so assigned are written above each letter. Each string of letters (the words, in this case) represents a number obtained by summing the letter values. These 7 results are recorded in blue on the bottom line. Their sum - the verse characteristic value - is 2701.

We shall be concerned only with the characteristic values (CVs) of the words. The following table defines a simple division of these CVs - the active numbers again being represented in blue:

The ordered set of seven CVs together with their total, 2701, occupies the first column (headed 'A'). Columns B and C, respectively, contain the odd- and the even-numbered members of the set with their totals, 1690 and 1011.

These totals factorise as follows:

• 1690 = 10 x 169; 169 being bifigurate, viz 13th rhombus/square and 8th hexagon; our interest here is in the latter configuration of 169 counters - depicted below in blue

• 1011 = 3 x 337; 337 being monofigurate with hexagram symmetry - specifically, 8th hexagram - depicted below in orange

Observe the fact that these representatives of numerical geometry have the same order number and are therefore capable of participating in the generation of tessellated patterns. But how may 10 hexagons unite with 3 compatible hexagrams to produce a symmetrical figure? One possibility is depicted here:

Clearly, this has 3 axes of symmetry which pass through the centroid counter of the central hexagon - these having an angular displacement of 120 degrees (interestingly, 120 being itself a triangular number!). This layout is all the more remarkable when one recollects that the blue counters (which constitute the hexagons) relate to the sum of the 4 odd-numbered words, "In the beginning", "God", "the heaven" and "the earth"; and the orange counters to the sum of the 'evens', "created", (untranslatable) and "and".

Another possible realisation of this tessellated symmetry is as follows:

Again, because 10 (the number of hexagons) and 3 (the number of hexagrams) are themselves triangular numbers, one further arrangement is possible, viz:

Observe the introduction of 3 different shades of colour for the hexagons so as to clarify the structure of the core of this 'odd/even' realisation of the seven words of Genesis 1:1.

In conclusion, two further points can be made:

• 10 x 169 + 3 x 337 is the only hexagon/hexagram tessellation possible from combinations of the words.

• over the range n = 1 to 1000, the expression [10 x hexagon(n) + 3 x hexagram(n)] yields a triangular number only when n = 8; and that, of course, is the instance under discussion here.

Vernon Jenkins MSc

2001-05-29

Extended 2001-06-03

Addendum: Genesis 8:14 as a Tessellated Trefoil

It may be recalled that Genesis 8:14 - describing the state of the earth immediately following the Flood - also sums to 2701. The details - originally provided in the page 'New for Old ' - are reiterated here.

Remarkably, these words may be divided into two well-defined groups, having the same values (viz 1690 and 1011) as those of Genesis 1:1, thus:

Clearly, each of the earlier trefoil realisations apply equally to this verse.

Vernon Jenkins MSc

2001-11-19

Acknowledgement: The author is indebted to Iain Strachan who discovered these trefoil associations.

email: vernon.jenkins@virgin.net

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