A sequence of six consecutive nines occurs in the
decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...
representation of the number
pi (), starting at the 762nd decimal place.
[.] It has become famous because of the
mathematical coincidence
A mathematical coincidence is said to occur when two expressions with no direct relationship show a near-equality which has no apparent theoretical explanation.
For example, there is a near-equality close to the round number 1000 between powers ...
and because of the idea that one could memorize the digits of up to that point, which seems to suggest that is
rational
Rationality is the quality of being guided by or based on reasons. In this regard, a person acts rationally if they have a good reason for what they do or a belief is rational if it is based on strong evidence. This quality can apply to an abili ...
. The earliest known mention of this idea occurs in
Douglas Hofstadter
Douglas Richard Hofstadter (born February 15, 1945) is an American scholar of cognitive science, physics, and comparative literature whose research includes concepts such as the sense of self in relation to the external world, consciousness, an ...
's 1985 book ''
Metamagical Themas
''Metamagical Themas'' is an eclectic collection of articles that Douglas Hofstadter wrote for the popular science magazine ''Scientific American'' during the early 1980s. The anthology was published in 1985 by Basic Books.
The volume is subst ...
'', where Hofstadter states
This sequence of six nines is sometimes called the "Feynman point", after physicist
Richard Feynman
Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superflu ...
, who allegedly stated this same idea in a lecture.
[.] 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
James Gleick (; born August 1, 1954) is an American author and historian of science whose work has chronicled the cultural impact of modern technology. Recognized for his writing about complex subjects through the techniques of narrative nonficti ...
.
Related statistics
is
conjecture
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 19 ...
d to be, but not known to be, a
normal number
In mathematics, a real number is said to be simply normal in an integer base b if its infinite sequence of digits is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b. A number is said to b ...
. For a normal number sampled uniformly at random, the probability of a specific sequence of six digits occurring this early in the decimal representation is about 0.08%.
[
The early string of six 9's is also the first occurrence of four and five consecutive identical digits. The next sequence of six consecutive identical digits is again composed of 9's, starting at position 193,034.][ The next distinct sequence of six consecutive identical digits starts with the digit 8 at position 222,299.][
]
Decimal expansion
The first 1,001 digits of (1,000 decimal places), showing consecutive runs of three or more digits including the consecutive six 9's underlined, are as follows:
See also
* 0.999...
* 9 (number)
9 (nine) is the natural number following and preceding .
Evolution of the Arabic digit
In the beginning, various Indians wrote a digit 9 similar in shape to the modern closing question mark without the bottom dot. The Kshatrapa, Andhra and ...
* Mathematical coincidence
A mathematical coincidence is said to occur when two expressions with no direct relationship show a near-equality which has no apparent theoretical explanation.
For example, there is a near-equality close to the round number 1000 between powers ...
* Repdigit
In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of repeated and digit.
Example ...
* Ramanujan's constant In number theory, a Heegner number (as termed by Conway and Guy) is a square-free positive integer ''d'' such that the imaginary quadratic field \Q\left sqrt\right/math> has class number 1. Equivalently, its ring of integers has unique factoriza ...
References
External links
Feynman Point Mathworld Article
– From the 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 Dig ...
project.
{{Douglas Hofstadter
Pi
Recreational mathematics