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Lo Shu Tessellation in Magic Squares Discovery by Jain

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Near Perfect Golden Diamonds or Phi Rhombi in the LoShu Tessellation.

The above diagrams are formed by tiling 9 Magic Square of 3x3 at 0° Yantra Pattern (ie: as it is without any rotated superimpositions) side by side, with the condition that each successive or alternate pattern is tiled at a tilt of 90°. I have coloured in all the near perfect Phi Triangles such that they appear like diamonds or rhombi, thus the appropriate name: Phi Diamonds or Golden Diamonds or Golden Rhombus or Phi Rhombi. Meditation upon the negative space reveals 8pointed Malteselike Crosses and octagonal structures.
The Magic Square of 3x3 or LoShu Pattern @ 0 degree has 2 elongated triangles in its pattern, that is very close to being a Golden Phi Triangle.
If it was precise, the Phi Triangle would have an apex of 36° but upon calculation it is 36.86° which is less than 1 degree off precision.
In this case for artistic purposes, I will call it a Phi Triangle but noting that it is an approximation to this ideal form. Referring this to being Golden Triangles is a matter of artistic appreciation, rather than rigorous mathematical precision. (This angle can be easily calculated because the longest lines in the diagram are based on Root 5, being the hypotenuse or diagonal of a righttriangle whose lesser lengths are 1x2. The exact Isosceles Phi Triangle has a ratio of its base to its side lengths in the proportion of 1:1.618… and the approximated Phi Triangle in the LoShu pattern has its proportion in this ratio of Root 5 ÷ Root 2 = 2.236…÷ 1.414 = 1.581…).
Jain 108

posted by theminorkey41