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Geometric Properties
As before, the world was created with wisdom - and not just any wisdom, but perfect, divine wisdom. No surprise then that the opening verse also contains tremendous wisdom in its geometric properties and balances.Here is a brief introduction to this vast subject.
Some numbers are called "figurate numbers". They can be shown geometrically by taking points, or dots, and arranging them into a regular shape such as a triangle or a pentagon.
As we saw, Genesis 1:1 consists of 28 letters and the first word, Beresheit, has 6 letters. 6 and 28 are the 3rd and 7th triangle numbers respectively. These numbers 3 and 7 are at the core of Genesis 1:1
| Triangle Numbers | |||
| T1 | 1 | = | 1 |
| T2 | 1+2 | = | 3 |
| T3 | 1+2+3 | = | 6 |
| T4 | 1+2+3+4 | = | 10 |
| T5 | 1+2+3+4+5 | = | 15 |
| T6 | 1+2+3+4+5+6 | = | 21 |
| T7 | 1+2+3+4+5+6+7 | = | 28 |
| T8 | 1+2+3+4+5+6+7+8 | = | 36 |
| T9 | 1+2+3+4+5+6+7+8+9 | = | 45 |
| T10 | 1+2+3+4+5+6+7+8+9+10 | = | 55 |
| .. | ... | .. | |
| T37 | 1+2+3..+37 | 703 | |
| .. | ... | .. | |
| T73 | 1+2+3..+73 | 2701 | |
(Triangle numbers are called by master kabalist R.Moshe Kordevero "source numbers" (Mispar Mekori), i.e. a number formed from a beginning. Notice above how the number 1 is always at the head of a triangle number. Thus they hint that everything stems from the One, i.e. G-d [1])
Triangular numbers can be arranged in Triangle formation such as:
Genesis 1:1 has Gematria of 2701
2701 is the 73rd triangular number:
Genesis 1:1 has 28 letters. 28 is a triangular number.
The base of this triangle - ואת הארץ has Gematria of 703
703 is the 37th triangle:
| Center Point | ||
37 is the exact center point of 73
|
(i.e. for 73 dots side by side, the middle dot is the 37th)
Thus, T37 fits perfectly inside the center of T73:
Infinite Triangles
The letter expansion (Milui) of the base ואת הארץ = 703 gives 2701!| Letter Expansion of ואת הארץ | ||||||
| ץ | ר | א | ה | ת | א | ו |
| צדי דלת יוד | ריש יוד שין | אלף למד פי | הי יוד | תאו אלף ואו | אלף למד פי | ואו אלף ואו |
| 558 | 890 | 275 | 35 | 531 | 275 | 137 |
| Total=2701 | ||||||
Due to this symmetry, the same pattern can be repeated again.
And again and again like an infinite mirror.
All this infinite expansion from the symmetry in the verse! Interestingly, the 703 triangle is geometrically related to the 10th "star of David" number = 541 = "Yisrael".
For, both the 703 triangle and the 10th star of David have 37 rows and both share the same perimeter count of 108 dots (more on 108 another time, be'H).
Interestingly, the 2701st Triangle (1+2+3+..2701) = 3,649,051
| Sum of Thousands | 3+649+051 | = | 703 |
| Perimeter | 8,100=8+100 | = | 108 |
Perimeter of 73rd Triangle
Another interesting property of the 73rd Triangle (2701 dots). It's perimeter is 216 dots = 63 (6 is a perfect number). Interestingly, the 6th cube is the only cube whose surface area (as measured in unit squares) equals its volume (in unit cubes)[2]. Note also that the opening word in Genesis 1:1 has 6 letters and the rest of the verse has 6 words (see Zohar, Hakdama Bereisheit 9a).
Other Arrangements
There are many other interesting ways to arrange the 2701 dots of Gen.1:1, such as according to the balance of words.A few examples (discovered by Vernon Jenkins[2]):
Another example:
These former two are not so a-priori though. The following one is perhaps more interesting:
3-D Tetrahedrons
The outline of the inner 703 triangle also hints to a 3-D shape, namely, this 3-D tetrahedrons structure.The 4 Tetrahedrons (pyramids) of size 36 + the 703 base gives:
4×8436 + 703 = 34447 = 49 × 703 dots.
The Tetrahedrons hint to the hidden Merkaba of Shechinah (Divine presence), the Merkaba of Peace as we will discuss another time, be'H. When we do Teshuvah (return to G-d) we get inside of it and the peace comes upon us from above.
The 4 combined tetrahedrons also form a single tetrahedron, thus the pattern can repeat in the same way infinitely.
(we will talk more about this amazing structure in the section "6 Days and Sabbath")
Triangle - the Prime Polygon
Note that the Hebrew word for Triangle is Meshulash - משולש.The triangle is the most prime polygon and thus has many connections to wisdom and Genesis 1:1.
The Gematrias of משולש are:
| Standard Gematria | = | 676 | Ordinal Gematria | = | 73 | Small Gematria | = | 19 |
Interestingly, 2701 also points to 676 as follows:
| Center Point | ||
1351 is the exact center point of 2701
|
| Center Point | ||
676 is the exact center point of 1351
|
676 is the final center point since only odd numbers have center points.
Thus, 2701 points to 676 and 676 = 262, where 26 is the Gematria of G-d's Name (the Tetragramaton).
For the creation is all about the relationship between man and G-d
45 = אדם (man)
452 + 262 = 2701
Man is supposed to make G-d the innermost center point of his life and always be aware of Him (Shulchan Aruch 1:1). Then, man will infuse holiness in the entire creation and be a partner with G-d (Path of the Just ch.26, Shaarei Kedusha Gate 3).
Interestingly, the Ordinal Gematria of Genesis 1:1 (298) = The 26th Prime (101) + The 45th Prime (197)
Also interesting, we have seen previously that the Gematria of Torah = 611 and the first 611 digits of Pi sum to 2701. If we look at the 611th position of Pi:
| 4526356082778577134275778 |
| 611th position of Pi (notice 45 and 26) |
Star of David
Let us now look at some of the hexagram (star of David) properties of 2701.
Star of David figurates are made by combining two triangles. For example, 2 triangles of 28 to form a Star of David of size 37. Or 2 triangles of 55 to form a star of david of 73. (both 28/55 and 37/73 are important numbers in Genesis[4])Star of David numbers are given by the formula:
6n×(n − 1) + 1
| Star of David (Hexagram) Numbers | |||
| ST1 | 6×1×(1-1)+1 | = | 1 |
| ST2 | 6×2×(2-1)+1 | = | 13 |
| ST3 | 6×3×(3-1)+1 | = | 37 |
| ST4 | 6×4×(4-1)+1 | = | 73 |
| ST5 | 6×5×(5-1)+1 | = | 121 |
| ST6 | 6×6×(6-1)+1 | = | 181 |
| ST7 | 6×7×(7-1)+1 | = | 253 |
| ST8 | 6×8×(8-1)+1 | = | 337 |
| ST9 | 6×9×(9-1)+1 | = | 433 |
| ST10 | 6×10×(10-1)+1 | = | 541 |
Since both 37 and 73 are star numbers and 2701=37×73, then it is possible to make a "star of star" figurate out of 2701 points.
This is the one and only "star of stars" whose stars follow each other and are center points of each other (73 follows 37 and 37 is the center point of 73) - a unique phenomena in all math!
Notice also the shape of the blank spaces between the stars. It is the same shape as the pattern we saw above in the word balances. shown here in red:
This page was meant to be a brief introduction. There are many, many more hints in the perimeters, midpoints, balances, etc. etc. in these figures and also other shapes such as the hexagons. The wisdom which springs from this verse appears to be inexhaustible.
All this reminds us of what is surely one of the most beautiful examples of design in the natural world - snowflakes! Until recently, their beautiful shapes were unseen as they can only be seen through a microscope. Notice how these actual snowflakes display a Star of David. This is very typical of snowflakes.
73 = Wisdom Star
The Star of David means many things, one of them is uniting heavens and earth, man's job in the world. As mentioned, the Star of David is formed by the merging of two triangles, one from above looking down, one from below looking up, and the overlap is the unification. So the hexagonal around the central point is the main unification inner part.The hexagonal part in Star 73 is unique as it is the hexagonal 37, and 37 is both hexagonal and a Star of David (thus star 73 is a unique phenomena in all of math - no other star number's inner hexagon is also its inner star). Notice all these numbers represent the wisdom series - (73,37,19,10,1).
Thus the Star with 73 points has the inner star with 37 points which has an inner hexagon with 19 which has a central point that is the 10th point. So you can look at it in multiple ways, in any case, this central point of creation is Yud-10, the 10 Sefirot in 1.
(note: in the star of Israel (541) the inner hexagonal part is 271, the Gematria of pregnancy, הריון and relates to 2701).
Another matter with the Star of David is the 6 corners for 6 sides and the central point is the holy point that gives energy/existence to the entire thing (heard from Oren Evron, see also section "6 days and Sabbath"). Indeed, the initial Chochmah (wisdom) comes from above, it is the apriori underlying mind, the initial point of wisdom and understanding.
Wisdom Triangle
The world was created with "wisdom" (Targum Yerushalmi, Genesis 1:1). This is represented by the letter "Yud" which is like a point-dot.The Gematrias of "Wisdom" (חכמה) are:
| 73 | = | Wisdom | (Standard Gematria) |
| 37 | = | Wisdom | (Ordinal Gematria and center point of 73) |
| 19 | = | Wisdom | (Small Gematria and center point of 37) |
| 10 | = | Wisdom | (Small Gematria reduced, 1+9=10 and center point of 19) |
| 1 | = | Wisdom | (Small Gematria reduced reduced, 1+0=1 = the point of creation) |
Thus, the "wisdom" series is: 73,37,19,10,1
In triangular numbers:
| T73 | (73rd Triangle) | = | 2701 |
| T37 | (37th Triangle) | = | 703 |
| T19 | (19th Triangle) | = | 190 |
| T10 | (10th Triangle) | = | 55 |
| T1 | (1st Triangle) | = | 1 |
37 is the midpoint of 73 - thus the 37th Triangle (703 dots) fits in the exact center of the 73rd Triangle (2701 dots), see above picture (by Oren Evron)
(note that 2701 is the ONLY triangle whose center triangle (703) is equal to its sum of thousands, namely 2+701=703, a unique phenomena in all math)
19 is the midpoint of 37 - thus the 19th Triangle (190 dots) fits in the exact center of the 37th Triangle.
10 is the midpoint of 19 - thus the 10th Triangle (55 dots) fits in the exact center of the 19th Triangle.
10 is an even number and thus has no midpoint. Thus, this is the final destination. However, two 10th triangles (55 dots) mirror combine to form the Star of David of 73 dots! Thus, the final structure is the Wisdom Star of David itself which also has the wisdom series 73,37,19,10,1!! (see above picture).
Mirroring of 73rd Triangle
This mirroring of the final 10th triangle (55 dots) to form the wisdom star along with the mirror symmetries of 2701 = 37×73 suggests mirroring the entire 73rd triangle (2701 dots) to form a Star of David of 3601 dots.Interestingly, as we saw in chapter "Beyond Decimal" (see there Footnote 1), the Star of David of 3601 dots is a very special Star of David. It is the solution to the supreme mirror symmetry in the Base-73 number system, i.e. the wisdom base.
Also, interesting is that the three inner stars are the 4th,7th and 13th star numbers. Thus, the 10th star (Yisrael) fits exactly in between the 7th (yellow) and 13th star (blue) for a 3 skip sequence (Oren Evron). This needs more investigation.
Such beauty and elegant perfection, such brilliant ability to design so many structures simultaneously! Nothing like this exists even a tiny bit 1000 times anywhere ever, such sophistication and wisdom of Creation.
>> Next: 6 Days and Sabbath
Footnotes
- [1] from the book Otyot Machkimot by Rabbi David Leitner return to text
- [2] used with permission of Vernon Jenkins, picture by Bill Downie return to text
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