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Topic: Prime numbers and pi
Replies: 33   Last Post: Dec 10, 2012 3:43 PM

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 Franz Gnaedinger Posts: 330 Registered: 4/30/07
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.