Lost Pythagorean Sacred Geometry understanding material nature by mathematics

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400 units can encompass differing amounts of area.

Thin rectangle:
175x25=4375

In isoceles triangle w/ 36, 36, 108 angles:
x+x+x(phi)=400
x=110.557
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Area = ~5,812

In the rectangle,
150x50=7,500

In equilateral triangle,
(√(3)/4)(133.333)^2=7,698

In the square,
100x100=10,000

In a pentagon,
(5*80^2) / (4√(5-2√5)) = 11,011

In a circle,
(400^2) / (4 π) = 12,732


Put 1, 1, 36 in the first three fields to represent two sides and the degree. You find the output to be phi.
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The same reason why where it's cold being bulky has its advantages. The more sphere-like the more volume relative to its surface area.

Reposting From Other Thread (deleting it there):



Origins of geometry and primitive proof of quality over quantity. Proportion over size.

A 100x100 area is more substantial than a 150x50 area.

Also of possible relevance to the phenemonon:

Fractal coastlines




Here is Wheeler describing the concept of "middle", proportion, found in ancient Greece; qua the divided line theory and phi. The origin of "hygiene" is symmetry and proportion,  not "cleanliness". The middle of a triangle is not the middle of its largest side. Connects it to water molecule somehow.



Quantitative vs Qualitative space. The former splits a triangle down the middle of its longest line. The latter splits the triangle such that each piece maintains the same dimensions/proportion.

Through my exploration of this, I sought to find the formula for an area of an isosceles triangle, given one only has its perimeter and its internal angles. Specifically so I could prove the proportional relevance of 1/phi.

Here is the formula:
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a=area, d=vertex angle,p= perimeter

No other fruits yet for my inquiry, except that one may prove the equation for Plato's divided line is x+y+y+z holds true, given the rules of proportional division he specifies. That is, there will always be two parts of same length when one divides a line (point-line, where geometric points are nonexistent absolutes) and the resultant portions all by the same proportions. I demonstrated this with an 18 unit line, which divided into 12/6, then 8/4/4/2. Perhaps one could divide a line in 1/9, then it'd be .1/.9/.9/8.1
... Appears it still holds true.

Thus a conclusion: Arbitrary divisions, repeated precisely as before (twice more*) equally onto the parts of the first division, begets an orderly pair; a sameness, repetition.

*Quantitatively, it is twice more. this involves time. Qualitatively, it is only once, as a pattern, which is there as a proporty(property/qualia,proportion).

With regard to Wheeler, 1 is a reification of no-thing. A void, reified into its opposite: every-thing. As a void has sameness and only sameness with the absence of thinginess - and 0 is absurd in representative mathematics (although one could argue 1 is just as absurd in reality), 1 also has only sameness with itself. Using 1 as a representation for the 'emergent' order of repeated and equal division is appropriate. 0 appears incompatible with the human mathematical system, when utilizing divisions. 0/x appropriately always gets 0, and x/1 appropriately always returns the same number x. 1 is a mirror of proporty. The addition and subtraction of 1 is the addition and subtraction of potential for the absorption of proporties.

The boy with incredible Brain (Super Genius Documentary)