Feynman point

Feynman point

The Feynman point is the sequence of six 9s which begins at the 762nd decimal place of π. It is named after physicist Richard Feynman, who once stated during a lecture he would like to memorize the digits of π until that point, so he could recite them and quip "nine nine nine nine nine nine and so on."Arndt, J. and Haenel, C. "Pi — Unleashed". Springer, p. 3, 2001. ISBN 3-540-66572-2.] Wells, D. "The Penguin Dictionary of Curious and Interesting Numbers". Middlesex, England: Penguin Books, p. 51, 1986. ISBN 0-14-026149-4.] The humorous irony of this statement is the suggestion that π is in fact rational, since this is falsely implied by an apparently infinitely recurring sequence of 9s.

Full decimal expansion

The full digits of π up to and including the Feynman point are as follows. [ [http://www.joyofpi.com/pi.html The Digits of Pi — First ten thousand] ]


Related statistics

For a randomly chosen real number, the probability of six 9s occurring this early in the decimal representation is only 0.08%.

The next sequence of six consecutive digits is again composed of 9s, starting at position 193,034. The next distinct sequence of six consecutive digits starts with 8 at position 222,299. Of the remaining digits, 0 is the last to first repeat 6 times, starting at position 1,699,927.

The Feynman point is also the first occurrence of four and five consecutive digits. The next appearance of four consecutive digits is of the digit 7 at position 1,589. [See, for example, the online [http://www.angio.net/pi/bigpi.cgi Pi Search] .]

The positions of the first occurrences of strings of 1, 2, ..., 9 consecutive 9s are 5; 44; 762; 762; 762; 762; 1,722,776; 36,356,642; and 564,665,206; respectively OEIS|id=A048940.

References

ee also

* Piphilology
* Richard Feynman
* Repdigit

External links

* [http://mathworld.wolfram.com/FeynmanPoint.html Feynman Point Mathworld Article] — From the Mathworld project.
* [http://www.angio.net/pi/piquery The Pi-Search Page] — Search the digits of pi.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • Feynman point — noun An anomaly in pi starting at the 762nd digit after the decimal point where there are six consecutive nines …   Wiktionary

  • Feynman — may refer to: * Richard Feynman ** Feynman diagram ** Feynman graph ** Feynman Kac formula ** The Feynman Lectures on Physics ** Feynman( s) (path) integral, see Path integral formulation ** Feynman parametrization ** Feynman checkerboard **… …   Wikipedia

  • FEYNMAN (R. P.) — Physicien américain, Richard Feynman a façonné la théorie des processus mettant en jeu les particules élémentaires. Sa contribution la plus déterminante est l’achèvement de l’électrodynamique quantique dans un cadre cohérent satisfaisant les… …   Encyclopédie Universelle

  • Feynman diagram — The Wick s expansion of the integrand gives (among others) the following termNarpsi(x)gamma^mupsi(x)arpsi(x )gamma^ upsi(x )underline{A mu(x)A u(x )};,whereunderline{A mu(x)A u(x )}=int{d^4pover(2pi)^4}{ig {mu u}over k^2+i0}e^{ k(x x )}is the… …   Wikipedia

  • Richard Feynman — Feynman redirects here. For other uses, see Feynman (disambiguation). Richard P. Feynman Richard Feynman at Fermilab Bor …   Wikipedia

  • Feynman , Richard Phillips — (1918–1988) American theoretical physicist The father of Feynman had been brought with his immigrant parents from Minsk, Byelorussia, in 1895. Feynman himself was born in New York and educated at the Massachusetts Institute of Technology and at… …   Scientists

  • Feynman graph — A Feynman graph is a graph suitable to be a Feynman diagram in a particular application of quantum field theory. (The most common use is when each field has quanta (particles) associated with it as the quantum of the electromagnetic field is a… …   Wikipedia

  • Feynman — Richard Feynman Richard Phillips Feynman Richard Feynman (au centre) avec Robert Oppenheimer (à sa gauche) à Los Alamos à l époque du projet Manhattan. Naissance …   Wikipédia en Français

  • Feynman, Richard P. — ▪ American physicist in full  Richard Phillips Feynman   born May 11, 1918, New York, New York, U.S. died February 15, 1988, Los Angeles, California       American theoretical physicist who was widely regarded as the most brilliant, influential,… …   Universalium

  • Point particle — Standard model of particle physics Standard Model …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”