Archive for October 7th, 2008

Today in Pi

October 7, 2008

Happy Decimal Digits 23,913,007 through 23,913,015 of Pi day! Yes, at the 23,913,007th digit (not counting the 3) is the string 10/07/2008 [precisely, …95510072008255…]. Apparently being only 24 million digits in in a bit of a lucky stroke: tomorrow’s date of 10/08/2008 first appears 100 million digits later, at the 124,023,083th place. (See Pi-Search for more such fun.)

Then I stared wondering about e. Sadly, being the less famous relation of π has its drawbacks and e doesn’t have its own search page. There is, however, a list of the first two million digits of e, which includes 1007 for 10/07, but not 10072008. Bummer we weren’t writing this a year ago: the string 10/7/2007 manages to squeeze in towards the end.

(The string 360 is much more popular: it starts at the 285th decimal digit in the expansion of pi, and occurs almost immediately in e: 2.7182818284590452353602874…)

Suppose you want to look for a name instead? Dr. Mike has translated 31,415,929 digits of pi and 27,182,818 digits of e into Base 27, to represent the 26 letters and punctuation. The laws of probability make long names hard to find, and even with all those digits GODZILLA doesn’t appear in the translated numbers (nor does MOTHRA), though a lot of other words do, as he explains at the bottom of each page. Interestingly, Dr. Mike used \sum \frac{1}{n!} in base 27 to estimate the digits of e. Hooray for Calc II and series convergence!