The Feynman point is a sequence of six 9s that begins at the 762nd decimal place of the decimal

Decimal

The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

 representation of

Pi

' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...

. It is named after physicist Richard Feynman

Richard Feynman

Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...

, who once stated during a lecture he would like to memorize the digits of until that point, so he could recite them and quip "nine nine nine nine nine nine and so on", suggesting, in a tongue-in-cheek

Tongue-in-cheek

Tongue-in-cheek is a phrase used as a figure of speech to imply that a statement or other production is humorously intended and it should not be taken at face value. The facial expression typically indicates that one is joking or making a mental effort. In the past, it may also have indicated...

 manner, that is rational

Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number...

.

Related statistics

is conjectured, but not known, to be a normal number

Normal number

In mathematics, a normal number is a real number whose infinite sequence of digits in every base b is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b, also all possible b2 pairs of digits are equally likely with density b−2,...

. For a randomly chosen normal number, the probability of any chosen number sequence of six digits (including 6 of a number, 658020, or the like) occurring this early in the decimal representation is only 0.08%.

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

The Feynman point 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.

The positions of the first occurrences of 9, alone and in strings of 2, 3, ..., 9 consecutive 9s, are 5; 44; 762; 762; 762; 762; 1,722,776; 36,356,642; and 564,665,206; respectively .

The number 2 (sometimes referred to by the greek letter (tau

Tau (2π)

Tau is a mathematical constant equal to the ratio of any circle's circumference to its radius, and has a value of approximately 6.28318531. This number also appears in many common formulas, often because it is the period of some very common functions — sine, cosine, , and others that involve...

)) has a corresponding sequence of seven consecutive 9s beginning at position 761. By contrast, the first appearance of seven consecutive copies of any digit in is 3333333 at position 710,100.

Full decimal expansion

The digits of up to three digits beyond the Feynman point are as follows:

See also

• Piphilology
  Piphilology
  Piphilology comprises the creation and use of mnemonic techniques to remember a span of digits of the mathematical constant . The word is a play on Pi itself and the linguistic field of philology....
  
  
• Repdigit
  Repdigit
  In recreational mathematics, a repdigit is a natural number composed of repeated instances of the same digit, most often in the decimal numeral system....
  
  
• 0.999...
  0.999...
  In mathematics, the repeating decimal 0.999... denotes a real number that can be shown to be the number one. In other words, the symbols 0.999... and 1 represent the same number...
  
  
• Ramanujan's constant
• Mathematical coincidence

External links

• Feynman Point Mathworld Article — From the Mathworld
  MathWorld
  MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at...
  
  project.
• The Pi-Search Page — Search the digits of pi.