Newton's Light Cube 2

Continued from page 1
Quadrature has eluded mathematicians until because they have been using Euclidean Geometry. You can only ever get a close approximation unless you use my geometry of complex space!

Here are the ways in which you can create a cube

Solution # 1 :
Circular Projective Geometry
A new projective geometry based upon circles.
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Solution # 2 :
Algebraic Equation for a square

 r^n = x^n + y^n

as n approaches infinity and r^n = constant.
Interesting as when n = 2 we have a circle. This allows for a complete transformation into a square but we need to take an infinite number of steps.
Fortunately my new geometry of complex space allows this to happen automatically.
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Solution # 3 :
The Polar Form of a Square
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Solution # 4 :
The Fourier Series Square
It has long been known you can get a square waveform this way. By combining three orthogonal fourier waves you can easily get a cube. I investigat if there are simple trigometric functions that could do the same.
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Solution # 5 :
The Interpretation of i^2 = -1
I will not repeat myself here but just remind you that this removes the need for tricky mathematical solutions.
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Solution # 6 :
The Extension of Archimedes Triangle. Archimedes (the great man himself) could not find the last step in his work. He got as far as converting a circle into a triangle with equal area to a square. I complete his work by using TWO circles!

Circular Projective Geometry - Continued on Page 3