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How Fibonacci numbers shape the 3-dimensional Sri Yantra
Figure 1. In
the 3-d Sri
Yantra, the 87 corners of 43 triangles
surround the centre
Figure 2. The 89 points needed to construct the 3-d Sri Yantra comprise the 34 tips of the 34 triangles in the 2nd, 3rd & 4th layers and 55 other points.
(All numbers in the text below that are Fibonacci numbers are coloured violet).
Some of the corners of triangles in the layers of the pyramidal, or 3-dimensional, Sri Yantra lie vertically above corners of triangles in adjacent layers. Such pairs of corners are denoted by pairs of differently coloured half-circles in the two diagrams above. The central triangle lies directly above the first layer of eight triangles. Above it is the so-called "bindu" (black dot), known as "Sarva Anandamaya," which represents the Absolute, the source of the Divine Creation mapped by the Sri Yantra. The numbers of corners of triangles in the various layers shown in Figure 1 are:
Central triangle: 3 white corners;
Layer 1: (8+8=16) violet corners of 8 violet triangles;
Layer 2: (10+20=20) blue corners of 10 blue triangles;
Layer 3: (10+10=20) yellow corners of 10 yellow triangles;
Layer 4: (14+14=28) red corners of 14 red triangles.
(3+16+20+20+28=87) corners of (1+8+10+10+14=43) triangles surround the centre (shown as a black circle) of the central triangle, above which hovers the bindu as a single point. 87 is the number value of Levanah, the Mundane Chakra of Yesod, which is the penultimate Sephirah of Construction. The 3-dimensional Sri Yantra constitutes a system of (1+1+87=89) points when the centre of the central triangle and the bindu above it are included. The number 89 is the 11th member of the well-known Fibonacci sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ...
This is an infinite series of positive integers whose nth members an are defined by: an = an−1 + an−2, where a0 = 0 and a1 = 1. Given that the bindu is an independent point that — in the pyramidal Sri Yantra — lies on the vertical axis passing through the centre of the central triangle, the latter point is needed to define this axis orthogonal to the four parallel layers of triangles so as to fix the position of the bindu relative to them. This means that a minimum number of 89 points is needed to construct the 43 triangles of the Sri Yantra in three dimensions when they are stacked one above the other in four sheets or layers. The bindu corresponds to the Fibonacci number 1, the first member of the sequence, whilst the centre of the central triangle corresponds to the second member, which is also 1. In Figure 2, the 89 points consist of the 34 green tips of the (10+10+14=34) triangles in layers 2, 3 & 4 and 55 other points/corners. The latter comprise 34 brown corners at the bases of the 34 triangles in layers 2, 3 & 4 and 21 points/corners made up of the 16 corners of the eight triangles in layer 1, namely, eight orange tips & eight violet corners at their bases, the three white corners of the central triangle, its centre (black circle) and the bindu (black dot) hovering directly above it.
We see that all the Fibonacci numbers up to 89 measure various sets of points that shape the geometry of the 3-dimensional Sri Yantra. If these sets had been created by a highly contrived selection of points, there would, obviously, be no significance to this pattern of Fibonacci numbers in the Sri Yantra because of the lack of natural underpinning of these points by its geometry. But this is not the case here. The first 11 Fibonacci numbers are compounded from corners of complete sets of triangles in the layers, not from odd bits and pieces of them picked in order to generate the right numbers. The correlation between these numbers and the geometrical features of the Sri Yantra that underpin them is natural, not artificial. It is implausible, therefore, to suggest that it could be just coincidence that there are 89 points, of which 21 points do not belong to the last three layers of triangles and 55 are not tips of the atter, leaving 34 points that are tips. Readers should ask themselves: what is the likelihood of four consecutive, Fibonacci numbers appearing by chance in such a natural manner?
The 43 triangles have 129 sides, where 129 is the number value of YAHWEH SABAOTH, the Godname of Netzach. The 42 triangles in the four separate layers have 84 corners, where
84 = 12 + 32 + 52 + 72,
and 126 sides, i.e., (84+126=210=21×10) corners & sides, showing how EHYEH, the Godname of Kether with number value 21, prescribes the 3-dimensional Sri Yantra. Therefore, 84 points and (126+42=168) lines & triangles surround the central triangle. This is one way in which the Sri Yantra embodies the superstring structural parameters 84 & 168 (for other ways, see Superstrings as sacred geometry/Sri Yantra). (87+129=216) points & lines surround the axis that passes through the bindu and the centre of the central triangle. 216 (=63) is the number of Geburah, which is the sixth Sephirah of Construction, counting from Malkuth.
When all the 43 triangles are Type A, the centres of the 42 triangles surrounding the central one become added to the 89 points, generating 131 points, where 131 is the number value of Samael, the Archangel of Geburah. Each Type A triangle has 15 hexagonal yods, so that the number of hexagonal yods in these 42 triangles = 42×15 = 630. Alternatively, Table 6 in Article 35 proves that 630 yods line the boundary of the 126 tetractyses that make up the 42 Type A triangles surrounding the central triangle. This is the number value of Seraphim, the Order of Angels assigned to Geburah. Notice also that, as the tips of six of the 14 triangles in the fourth layer touch the circle circumscribing the base of the pyramidal Sri Yantra, (42−6=36) of the 42 triangles do not touch it. The value of ELOHA, the Godname of Geburah, is 36. We find that four number values referring to the same Sephirah, namely, 216, 36, 131 & 630, emerge naturally from simple considerations of the geometrical composition and yod populations of the 3-dimensional Sri Yantra. Such an amazing conjunction of numbers cannot, plausibly, be dismissed as coincidence. Instead, it arises because the source of the Sri Yantra revelation as a yantra sacred to Hindus is the same as the source of the Kabbalah, the mystical teachings of Jews. This source is the Mind of God, which may be accessed by humans during mystical states of consciousness and which provides the archetypal components of the "Perennial Philosophy" — the esoteric tradition at the heart of the world's religions.
See Article 50 (Part 1) & Article 50 (Part 2) for analysis of the way in which other sacred geometries embody Fibonacci numbers.
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