Six nines in pi: Difference between revisions
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[[Image:Pi digits distribution.png|thumb|right|Pi's first few hundred digits contain (expectedly) ample double consecutive (marked yellow) digits, and a few triple consecutive (marked green) digits. The early presence of six consecutive digits (marked orange), dubbed the "Feynman Point," is intriguing.]] |
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The '''Feynman Point''' is the sequence of six |
The '''Feynman Point''' is the sequence of six 9's which begins at the 762<sup>nd</sup> decimal place of [[π]]. It is named after physicist [[Richard Feynman]], who once stated 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."{{fact}} |
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The full digits of π up to the Feynman Point are as follows. |
The full digits of π up to the Feynman Point are as follows.<ref>http://www.joyofpi.com/pi.html</ref> |
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3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214 |
3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214 |
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477130996051870721134'''999999''' |
477130996051870721134'''999999''' |
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The positions of the first occurrences of strings of 1, 2, ... consecutive |
The positions of the first occurrences of strings of 1, 2, ..., 9 consecutive 9's are 5, 44, 762, 762, 762, 762, 1722776, 36356642, and 564665206, respectively.<ref>Wells, D. ''The Penguin Dictionary of Curious and Interesting Numbers''. Middlesex, England: Penguin Books, p. 51, 1986.</ref> |
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For comparison, the next sequence of 6 repeated digits starts with 8 at position 222,299. |
For comparison, the next sequence of 6 repeated 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. |
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==References== |
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<references/> |
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==See also== |
==See also== |
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* [[Pi]] |
* [[Pi]] |
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* [[Piphilology]] |
* [[Piphilology]] |
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* [[Richard Feynman]] |
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==External links== |
==External links== |
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* [http://mathworld.wolfram.com/FeynmanPoint.html Feynman Point Mathworld Article] - From the [[Mathworld]] project. |
* [http://mathworld.wolfram.com/FeynmanPoint.html Feynman Point Mathworld Article] - From the [[Mathworld]] project. |
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* [http://www.angio.net/pi/piquery The Pi-Search Page] - Search the digits of pi. |
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[[Category: pi]] |
[[Category: pi]] |
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Revision as of 22:07, 25 November 2006
The Feynman Point is the sequence of six 9's which begins at the 762nd decimal place of π. It is named after physicist Richard Feynman, who once stated 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."[citation needed]
The full digits of π up to the Feynman Point are as follows.[1]
3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214 8086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975 6659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155 8817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309 2186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394 9463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577 8960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977 477130996051870721134999999
The positions of the first occurrences of strings of 1, 2, ..., 9 consecutive 9's are 5, 44, 762, 762, 762, 762, 1722776, 36356642, and 564665206, respectively.[2]
For comparison, the next sequence of 6 repeated 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.
References
- ^ http://www.joyofpi.com/pi.html
- ^ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 51, 1986.
See also
External links
- Feynman Point Mathworld Article - From the Mathworld project.
- The Pi-Search Page - Search the digits of pi.