
Re: Prime numbers and pi
Posted:
Apr 23, 2009 1:25 AM


Mathematics is based on the equation
a = a
while the world is ruled by Goethe's formula
all is equial, all unequal
An apple is an apple, but one apple may be small and red, another big and yellow. The logic of mathematics is the one of building and maintaining. If the bricks have the same size, if the are equal, b = b = b = b = b = ..., a wall is easily built, and if they are stable, keep their shape, neither soak up rain nor crumble in the summer sun, remaining as they are, the wall will stand.
In the light of the basic equation a = a the world appears as a pattern of patterns of pattern of patterns. I see a direct line from the Egyptian unit fraction series to Euler:
1 = 1
1 = '1 1 = '2 '2 1 = '2 '4 '4 1 = '2 '4 '8 '8
1 = '2 '4 '8 '16 '32 '64 ...
1 = '1 1 = '1x2 '2 1 = '1x2 '2x3 '3 1 = '1x2 '2x3 '3x4 '4
1 = '1x2 '2x3 '3x4 '4x5 '5x6 ...
'2 = '2 '2 = '1x3 '6 '2 = '1x3 '3x5 '10 '2 = '1x3 '3x5 '5x7 '14
'2 = '1x3 '3x5 '5x7 '7x9 '9x11 ...
'1x3 '16 '1x3 '5x7 '32 '1x3 '5x7 '9x11 '48 '1x3 '5x7 '9x11 '13x15 '64
'1x3 '5x7 '9x11 '13x15 '17x19 ... = pi/8
'2 minus '3x5 '24 '2 minus '3x5 '7x9 '40 '2 minus '3x5 '7x9 '11x13 '56 '2 minus '3x5 '7x9 '11x13 '15x17 '72
'2 minus '3x5 '8x9 '11x13 '15x17 '19x21 ... = pi/8
"1 '1x1 "3 '1x1 '2x2 "5 '1x1 '2x2 '3x3 '4x4 "7
'1x1 '2x2 '3x3 '4x4 '5x5 '6x6 ... = pi x pi / 6
= 4/3 x 9/8 x 25/24 x 49/48 x 121/120 x 169/168 ...
There will be more mathematicians like the author of the lost original of the Rhind Mathematical Papyrus and Leonhard Euler, as there are infinitely many patterns created by the formula a = a, patterns of patterns of patterns revealed by the basic equation of mathematics and the light of mathematical logic.

