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

 Messages: [ Previous | Next ]
 Franz Gnaedinger Posts: 330 Registered: 4/30/07
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