Today in Pi

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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!

6 Responses to “Today in Pi”

  1. Batman Says:

    The e page does have 100708 for 10/07/08, though, in three places. It also has 100808 in three places. It also has 31415, but not 314159, and it has 141592, but not 1415926. On the other hand, π has 27182818, starting at position 73,154,827. Yeah, I’m bored.

  2. Ξ Says:

    And there’s even more flexibility with other standard date formats: 08102008 (for 08 October 2008) is 52 million digits in in the expansion of pi (as prof_hobart pointed out on reddit this morning). [Neither 08102008 nor 081008 appear in the e digits, though 08/10/08 is a cooler looking date than 10/08/08].

  3. TwoPi Says:

    Appropriately, “Euler” appears in the expansions of both pi and e (as does “Erdos”). For what it’s worth [trust me, not much], “TwoPi” also appears in the expansions for pi and e. So I’m in good company, and “there goes the neighborhood” quoth E and E.

    “Hamlet” does not appear in the tens of millions of digits being used for e and pi, but I trust that it (along with the full text of the play itself, in english, spanish, and latin) will eventually appear in each.

    Sagan suggested looking for graphs of circles in the binary expansion of pi, and presumably we’d eventually find them, no? I’d be curious to hear suggestions for similar graphs related to exponential growth to hunt for in the digits of e. My vote: a tree diagram.

  4. Top Posts « WordPress.com Says:

    […] Today in Pi 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 […] […]

  5. Mona Says:

    i have a report about pi..
    please help me!!!

  6. Ξ Says:

    Hi Mona! What kind of things are you looking for?

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