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**#73 Correspondence between the 2nd-order tetractys and the
1-tree**

The 2nd-order tetractys comprises 85 yods, where

85 = 4^{0} + 4^{1} + 4^{2} + 4^{3}.

The three 1st-order tetractyses at its corners representing the Supernal Triad contain 30 yods, where

30 = 1^{2} + 2^{2} + 3^{2} + 4^{2},

so that the seven 1st-order tetractyses representing the seven Sephiroth of Construction have (85−30=55) red yods, where

55 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10

is both the *tenth* triangular number and the *tenth* Fibonacci number
in the Fibonacci sequence:

1, 1, 2, 3, 5, 8, 13, **21**, 34, 55, 89, 144, 223, ...

This is also the number of points, lines & triangles in the 2nd-order tetractys (see the
diagram above), showing how this Pythagorean representation of holistic systems embodies the number 55. Moreover,
as each triangle is composed of three corners, three sides & one triangle, i.e., seven geometrical elements,
the blue triangles at the corners of the 2nd-order tetractys comprise **21** geometrical
elements, leaving 34 geometrical elements making up the seven red triangles, i.e., 55 = **21** +
34. The number **21** is the eighth Fibonacci number and 34 is the ninth Fibonacci number. The
1-tree is composed of 11 corners and 25 sides of 19 triangles, i.e., 55 geometrical elements. Its Upper Face (the
blue kite shape with Kether, Chokmah, Binah, Daath & Tiphareth at its corners) comprises five blue points, nine
blue lines & seven blue triangles, i.e., **21** geometrical elements; the remainder of the
1-tree comprises six red points, 16 red sides & 12 red triangles, i.e., 34 geometrical elements. The Upper Face
with **21** geometrical elements corresponds to the three blue triangles with
**21** geometrical elements at the corners of the 2nd-order tetractys symbolising the Supernal
Triad, whilst the rest of the 1-tree with 34 geometrical elements corresponds to the 34 geometrical elements making
up the seven red triangles that symbolise the seven Sephiroth of Construction. The appearance of three
*successive* Fibonacci numbers in both the 2nd-order tetractys and the 1-tree is the manifestation of a
deeper connection between this type of number and the geometry of the n-tree because the number of geometrical
elements in the latter is

N(n) = 34n + **21**,*

where the kite shape formed by Tiphareth, Netzach, Hod, Yesod & Malkuth has
**21** geometrical elements, so that N(n+1) − N(n) = 34, i.e., 34 more geometrical elements
appear in successively overlapping Trees of Life. In particular, the 2-tree has (55+34=89) points, lines &
triangles, where 89 is the 11th Fibonacci number. The 34:**21** division reflects in the
2nd-order tetractys the distinction between the three blue triangles at its corners and the seven red triangles,
i.e., *between the Supernal Triad and the seven Sephiroth of Construction*. Many sunflowers have their
florets arranged in 55 spirals, 34 of which are clockwise and **21** are anticlockwise:

The florets in this sunflower lie on 34 clockwise spirals and **21** anticlockwise spirals.

Article 50 (Part 1) and Article 50 (Part 2) discuss how Fibonacci numbers shape other sacred
geometries. #8 at **Sacred geometry/Sri
Yantra** discusses how the 3-dimensional Sri Yantra embodies the Fibonacci numbers up to
89.

* Proof: the n-tree has (12n+7) triangles with (6n+5) corners and (16n+9) sides. Number of
corners, sides & triangles in the n-tree = (6+16+12=34)n + (5+9+7=**21**).

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