• Repeated digits in Pi -- the Feynman point

    From HenHanna@HenHanna@dev.null to rec.puzzles,sci.lang,sci.math on Sun Jun 22 19:15:32 2025
    From Newsgroup: sci.lang

    Yes, Richard Feynman and Raymond Smullyan were childhood
    friends. Both were born and raised in Far Rockaway, Queens, New York,
    and attended grade school together in the same neighborhood.
    Smullyan specifically mentions that he was a grade school
    classmate of Feynman. Their shared early environment in Far Rockaway is frequently noted in biographical accounts of both figures.


    ______________________________



    The Feynman point refers to the sequence of six consecutive
    nines (999999) that appears in the decimal expansion of pi (-C), starting
    at the 762nd digit after the decimal point. This point is notable
    because such a long run of identical digits is statistically rare so
    early in the sequence, leading to its fame as a mathematical curiosity.

    The name honors physicist Richard Feynman, who is said to have
    joked about memorizing pi up to that point and then mischievously
    claiming pi is rational by reciting the six nines and saying "and so
    on". However, there is no clear record of Feynman actually making this
    remark in a lecture, and the story has become part of mathematical
    folklore.

    ___________________________________________

    The remarkable repetition at digit #763 is called the Feynman
    point.


    Skipping 2 times...
    (skipping 4 repeats, and 5 repeats)
    doesn't seem all that remarkable.


    _______________________________________________
    Repeated digits in pi
    Walter Nissen
    Dec 5, 1995


    Since my last post, I have learned a bit about this problem, but very
    little. I thank each of the respondents for their help. This is what I
    know. 3 is the first single digit in pi. 33 is the first doubled digit.
    111 is the first tripled digit. From searches at Jeremy Gilbert's Web
    page, http://gryphon.ccs.brandeis.edu/~grath/attractions/gpi/index.html,
    I
    derive this table:

    digits digit #
    3 1
    33 25
    111 154
    999999 763
    3333333 710101

    http://cad.ucla.edu:8001/amiinpi confirms the first part of this.

    The remarkable repetition at digit #763 is called the Feynman point.

    Perhaps because the late, great Richard P. Feynman called attention to
    it??

    I would welcome any information about extension of this table,
    especially
    resources on the Net. What I have so far seems pitiful compared to the
    4G
    computed digits.

    Thanks.

    Cheers.

    Walter Nissen dk...@cleveland.freenet.edu
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