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Re: Prime numbers and pi
Posted:
Apr 27, 2009 2:15 AM


Milo, read the Rhind Mathematical Papyrus as written! Your method is not the one used by Ahmes. Consulting the 2/n table is not enough. How many times did I tell you so, and for how many years?

In a previous message I said the infinite product
1x4/2x3 x 7x10/8x9 x 13x16/14x15 ...
may equal 2/pi. Wrong. In another message I said the infinite product
1x3/2x2 x 5x7/6x6 x 9x11/10x10 ...
may equal ln2. Also wrong. It equals the inverse of the square root of 2 and is approximated by the stairway
3/4 x 16/17 3/4 x 35/36 x 32/33 3/4 x 35/36 x 99/100 x 48/49 3/4 x 35/36 x 99/100 x 195/196 x 64/65
Row 51 yields 0.70797384... x 816/817 = 0.707107287..., the square of which is 0.50000071...
The infinite product contains Euler's infinite pi product of the primes as factor
pi/2 = 3/2 x 5/6 x 7/6 x 11/10 x 13/14 x 17/18 x ...
while the inverse numerators of the stairway approximate pi/8
'3 '16 '3 '35 '32 '3 '35 '99 '48 '3 '35 '99 '195 '64
and yield the best results when combined with the complementary pattern
'2 minus '15 '24 '2 minus '15 '63 '40 '2 minus '15 '63 '143 '56 '2 minus '15 '63 '143 '255 '72



