Expressions for Pi |
| Expression | Source | Value |
|---|---|---|
| 3 | Bible | 3.0 |
| 3 + 1/7 | Greeks | 3.142857142857143 |
| 3 + 10/71 < pi < 3 + 1/7 | Archimedes | Lower: 3.140845070 Ave: 3.141851106 |
| 355/113 | Best Approximation | 3.1415929203539825 |
| 3+8/60+29/60^2+44/60^3 | 3.1415925925925925 | |
| (9*9 + 19*19/22)^(1/4) | Ramanajan | 3.141592652582646 |
| 3+1/(7+1/(15+1/(1+1/292))) | Continued fraction | 3.1415926530119025 |
| (3 log(5280)/sqrt(67) | 3.1415926529722977 | |
| (63/25)*(17+15*5^0.5)/(7+15*5^0.5) | 3.141592653805688 | |
| (3 log(640320)/sqrt(163) | 3.141592653589793 | |
| log(640320^3 + 744)/sqrt(427) | pi to 30 places | |
| log(5280^3(236674+30303 sqrt(61))^3 + 744)/sqrt(427) |
pi to 52 places | |
| 3+1/(7+1/(15+1/(1+1/(292+1/(1+1/(1+1/ (1+1/(2+1/(1+1/(3+1/(1+1/14))))))))))) |
Continued fraction | 3.1415926535897927 |
| 4/( 1+ 1^2/( 3+ 2^2/( 5+ 3^2/ ( 7+ 4^2/( 9+ 5^2/(11+ 6^2/ (13+ 7^2/(15+ 8^2/(17+ 9^2/ (19+10^2/(21+11^2/(23+12^2/ (25+13^2/(27+14^2/(29+15^2/ (31+16^2/(33+17^2/(35+18^2/ (37+19^2/(39+20^2/(41+21^2/ (43+22^2/ 45)))))))))))))))))))))) |
Continued fraction | 3.141592653589793 |
| (4 arctan(1)) | (Sort of cheating) | Exactly pi |