All those books that Google has been scanning for the past ten years are surprisingly rich in numbers as well as words. The Google Books data set released last December by a Harvard-Google team includes (by my count) 9,620,835,344 occurrences of 458,794 distinct numbers. (Plus another 31,293 numeric values that have dollar signs attached.)
In recognition of pi day, I want to zero in on some successive approximations to the world’s favorite irrational:
In tabular form here are the closest approximations found in the files, along with the abundance of each value:
| 3.141592 | 704 |
| 3.1415923 | 80 |
| 3.1415926 | 1141 |
| 3.14159265 | 1300 |
| 3.141592653 | 143 |
| 3.1415926535 | 286 |
| 3.141592653589 | 54 |
| 3.14159265358979 | 338 |
| 3.141592653589793 | 453 |
| 3.1415926535898 | 65 |
| 3.14159265359 | 177 |
| 3.1415926536 | 289 |
| 3.141592654 | 512 |
| 3.1415927 | 776 |
| 3.1415928 | 109 |
| 3.1415929 | 133 |
| 3.141593 | 843 |
The data set includes only items that appear at least 40 times in the collection of scanned volumes. Closer approximations to pi evidently fell below that threshold. In particular there is no sign of William Shanks’s famous 707-digit calculation, which was published in 1873. So, just for the sake of celebrating 3.14, here are 707 digits of pi—but unlike the product of Shanks’s many years of labor, I think these digits may be correct:
3.1415926535897932384626433832795028841971693993751058209
74944592307816406286208998628034825342117067982148086513
282306647093844609550582231725359408128481117450284102701
938521105559644622948954930381964428810975665933446128475
648233786783165271201909145648566923460348610454326648213
393607260249141273724587006606315588174881520920962829254
0917153643678925903600113305305488204665213841469519415116
09433057270365759591953092186117381932611793105118548074462
3799627495673518857527248912279381830119491298336733624406
5664308602139494639522473719070217986094370277053921717629
3176752384674818467669405132000568127145263560827785771342
7577896091736371787214684409012249534301465495853710507922
796892589235420200