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#28 The Type C pentagon geometrically embodies the fine-structure constant number 137


The Tree of Life pattern in the Type C pentagon

(137+137) geometrical elements outside root edge surround centres of two Type C pentagons


The Type C pentagon has 26 corners & 70 sides of 45 triangles, i.e., 141 geometrical elements. Two separate Type C pentagons have 282 geometrical elements, of which 50 are corners surrounding their centres. 282 is the number value of Aralim, the Order of Angels assigned to Binah, whose Godname ELOHIM has the number value 50. The number 70 is a parameter of holistic systems, being the number of yods in the Tree of Life when its 16 triangles are tetractyses. The five black sides of the pentagon and the five black sides of its sectors correspond to the (5+5) Sephirothic corners of these triangles. The 60 remaining red sides of the 45 triangles correspond to the 60 hexagonal yods in the Tree of Life constructed from tetractyses. This 10:60 pattern expresses the difference between Malkuth and the six higher Sephiroth of Construction in the outer Tree of Life. Its counterpart in its inner form is the dodecagon and the six regular polygons that precede it.


140 geometrical elements in the Type C pentagon surround its centre, where 140 is the number of Masloth, the Mundane Chakra of Chokmah, whose Godname YAHWEH has the number 26. 137 geometrical elements outside the root edge surround its centre. We see that the geometrical composition of the Type C pentagon embodies the number 137 determining the fine-structure constant α = e2/ħc ≅ 1/137 well-known to physicists, whilst the number of bones in the adult human skeleton is embodied in its yods other than its corners (see #27).


ELOHIM, the Godname of Binah, prescribes the pair of joined Type C pentagons because its number value 50 is the number of corners of their 90 triangles, whilst YAHWEH prescribes the 26 corners of the 45 triangles in each pentagon. The two joined Type C pentagons have 229 lines & triangles, where 229 is the 50th prime number. ELOHIM prescribes both the number of corners of the triangles in the two pentagons and the number of their sides & triangles!


The pair of joined Type C pentagons has 189 corners & sides, i.e., 187 corners & sides surround their two centres. 187 is the number of Auphanim, the Order of Angels assigned to Chokmah. 95 corners & sides in a Type C pentagon surround its centre, where 95 is the number value of Madim, the Mundane Chakra of Geburah. A corner of each pentagon coincides with the centre of the decagon when it is part of the inner Tree of Life. This means that surrounding the centre of each pentagon are 136 geometrical elements outside the shared root edge that are intrinsic to this polygon in the sense that they are not part of any other polygon in the inner Tree of Life. The pair of pentagons has 272 such geometrical elements, where 272 is the number value of Cherubim, the Order of Angels assigned to Yesod.


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