| 词条 | Six nines in pi | ||
| 释义 |
A sequence of six 9s occurs in the decimal representation of the number pi ({{pi}}), starting at the 762nd decimal place.[1] It has become famous because of the mathematical coincidence and because of the idea that one could memorize the digits of {{pi}} up to that point, recite them and end with "nine nine nine nine nine nine and so on", which seems to suggest that {{pi}} is rational. The earliest known mention of this idea occurs in Douglas Hofstadter's 1985 book Metamagical Themas, where Hofstadter states[2][3] {{quote|text=I myself once learned 380 digits of {{pi}}, when I was a crazy high-school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes "999999", so that I could recite it out loud, come to those six 9's, and then impishly say, "and so on!"|author=Douglas Hofstadter|source=Metamagical Themas}}This sequence of six nines is sometimes called the "Feynman point", after physicist Richard Feynman, who has also been claimed to have stated this same idea in a lecture.[4] It is not clear when, or even if, Feynman made such a statement, however; it is not mentioned in published biographies or in his autobiographies, and is unknown to his biographer, James Gleick.[5] Related statistics{{pi}} is conjectured to be, but not known to be, a normal number. For a randomly chosen normal number, the probability of a specific sequence of six digits occurring this early in the decimal representation is usually only about 0.08%.[4] However, if the sequence can overlap itself (such as 123123 or 999999) then the probability is less. The probability of six 9's in a row this early is about 10% less, or 0.0686%. But the probability of a repetition of any digit six times starting in the first 762 digits is ten times greater, or 0.686%.The early string of six 9's is also the first occurrence of four and five consecutive identical digits. The next appearance of four consecutive identical digits is of the digit 7 at position 1,589.[7] The next sequence of six consecutive identical digits is again composed of 9's, starting at position 193,034.[4] The next distinct sequence of six consecutive identical digits starts with the digit 8 at position 222,299,[6] while strings of nine 9's next occur at position 590,331,982 and 640,787,382.[7] The positions of the first occurrence of a string of 1, 2, 3, 4, 5, 6, 7, 8, and 9 consecutive 9's in the decimal expansion are 5; 44; 762; 762; 762; 762; 1,722,776; 36,356,642; and 564,665,206, respectively {{OEIS|id=A048940}}.[1] Decimal expansionThe first 1,001 digits of {{pi}} (1,000 decimal digits), showing consecutive runs of three or more digits including the consecutive six 9's underlined, are as follows:[8]
See also{{portal|Mathematics}}
References1. ^1 {{Citation |last=Wells |first=D. |title=The Penguin Dictionary of Curious and Interesting Numbers |location=Middlesex, England |publisher=Penguin Books |page=51 |year=1986 |isbn=0-14-026149-4 }}. 2. ^{{cite book | url=https://archive.org/stream/MetamagicalThemas/Metamagical%20Themas,%20Hofstadter_djvu.txt | title=Metamagical Themas | publisher=Basic Books | author=Hofstadter, Douglas | authorlink=Douglas Hofstadter | year=1985 | isbn=0-465-04566-9}} 3. ^{{cite news | url=https://www.washingtonpost.com/archive/entertainment/books/1985/05/05/douglass-hofstadters-pi-in-the-sky/88c04d3c-419c-4acd-9f32-e0ac2a92f3ff/ | title=Douglass Hofstadter's Pi in the Sky | work=The Washington Post | date=5 May 1985 | accessdate=4 January 2016 | author=Rucker, Rudy|author-link=Rudy Rucker}} 4. ^1 2 {{Citation |last=Arndt |first=J. |lastauthoramp=yes |last2=Haenel |first2=C. |title=Pi – Unleashed |location=Berlin |publisher=Springer |page=3 |year=2001 |isbn=3-540-66572-2 }}. 5. ^{{cite news | author = David Brooks | title = Wikipedia turns 15 on Friday (citation needed) | newspaper = Concord Monitor | url = http://granitegeek.concordmonitor.com/2016/01/12/wikipedia-turns-15-on-friday-citation-needed/ | date = 12 January 2016 | accessdate = 10 February 2016}} 6. ^1 Pi Search 7. ^calculated with editpad lite 7 8. ^The Digits of Pi — First ten thousand External links
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