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Re: Prime numbers and pi
Posted:
Apr 16, 2009 3:43 AM
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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.
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