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3.11 Hypergeometric inversions. 3.12 Miscellaneous. ... Value; Less than 22/7; ... A History of Pi; In culture; Indiana pi bill; Pi Day;
(Pi function) – the gamma function when offset to coincide with the factorial Rectangular function π ( n ) {\displaystyle \pi (n)\,\!} – the Pisano period
The number π (/ p aɪ /; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.
Of some notability are legal or historical texts purportedly "defining π" to have some rational value, such as the "Indiana Pi Bill" of 1897, which stated "the ratio of the diameter and circumference is as five-fourths to four" (which would imply "π = 3.2") and a passage in the Hebrew Bible that implies that π = 3.
In other words, the n th digit of this number is 1 only if n is one of the numbers 1! = 1, 2! = 2, 3! = 6, 4! = 24, etc. Liouville showed that this number belongs to a class of transcendental numbers that can be more closely approximated by rational numbers than can any irrational algebraic number, and this class of numbers is called the ...
Calculation made in Philadelphia, Pennsylvania, giving the value of pi to 154 digits, 152 of which were correct. First discovered by F. X. von Zach in a library in Oxford, England in the 1780s, and reported to Jean-Étienne Montucla , who published an account of it.
12 as: The best timing control of laser pulses. [7] 43 as: The shortest X-ray laser pulse [8] 53 as: The shortest electron laser pulse [9] [10] 10 −15: femtosecond: fs One quadrillionth of one second 1 fs: The cycle time for ultraviolet light with a wavelength of 300 nanometres; The time it takes light to travel a distance of 0.3 micrometres ...
Plot of the first 10,000 Pisano periods. In number theory, the nth Pisano period, written as π (n), is the period with which the sequence of Fibonacci numbers taken modulo n repeats.