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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 16, 2009 3:43 AM

Euler's infinite product in a modified form:

pi = 4 times 1x3/2x2 times 5x7/6x6 times 11x13/10x14
times 17x19/18x18 times 23x29/22x30 times 31x37/30x38
times 41x43/42x42 times 47x53/46x54 times 59x61/58x62
times 67x71/66x70 times ...

Checking the stairway:

4 x 4/3 = 5.333...

4 x 3/4 x 9/8 = 3.375

4 x 3/4 x 35/36 x 14/13 = 3.14102...

4 x 3/4 x 35/36 x 143/140 x 19/18 = 3.14467...

4 x ... x 323/324 x 24/23 = 3.09910...

4 x ... x 667/660 x 29/28 = 3.10866...

4 x ... x 1147/1140 x 34/33 = 3.11141...

4 x ... x 1763/1764 x 39/38 = 3.09761...

4 x ... x 2491/2484 x 44/43 = 3.09761...

4 x ... x 3599/3596 x 49/48 = 3.09232...

4 x ... x 4687/4620 x 54/53 = 3.13113...

Remarkble is the value 3.14102... in the third row.