The Alchemy Key.pdf - Veritas File System

the middle of the pyramid’s base on the ground plane has the same
perimeter as that base in plan view. The error is 0.096%.
We can even proceed a little further to find a solution to the
classic problem of ‘Squaring the Circle’. This is to find a technique of
drawing a circle with the same area as a given square, using only
geometric means. It has engaged mathematicians for many thousands of
years. 1461
Again, let the Perfect Pyramid be laid flat so the
sides splay into a Cross Patté. The area of a circle
inscribed within the Cross Patté is:
Area of Inscribed Patté Circle = π k 2
(pi x radius squared)
Substituting (1): k 2 = (s/2) 2 + h 2
Area of Inscribed Patté Circle π = [(s/2) 2 + h 2 ]
π = .s 2 [¼ + h 2 /s 2 ]
Substituting (6): h 2 /s 2 = Φ/4
Area of Inscribed Patté Circle = π.s 2 [¼ + Φ/4]
= ¼ . π.s 2 [1 + Φ]
The exceptional property of the Golden Ratio is that:
1 + Φ = Φ 2
Area of Inscribed Patté Circle = ¼ . π.s 2 [Φ 2 ]
Since the Area of the Base of the Perfect Pyramid is the side
length squared, s 2 :
Area of Inscribed Patté Circle = [¼ π.Φ . 2 ] x Area of Base
The value of [¼ π.Φ . 2 ] is 2.056199, almost the integer two.
Substituting the approximate value of two for [¼ π.Φ . 2 ] simplifies the
equation to:
Area of Inscribed Patté Circle ≈ 2 x Area of Pyramid
Base
With the Cross Patté, medieval mathematicians found an
approximate solution to squaring the circle. This was to take a Perfect
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