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355 / 113 is the best rational approximation of π with a denominator of four digits or fewer, being accurate to six decimal places. It is within 0.000 009 % of the value of π, or in terms of common fractions overestimates π by less than 1 / 3 748 629 .
Super PI by Kanada Laboratory [101] in the University of Tokyo is the program for Microsoft Windows for runs from 16,000 to 33,550,000 digits. It can compute one million digits in 40 minutes, two million digits in 90 minutes and four million digits in 220 minutes on a Pentium 90 MHz. Super PI version 1.9 is available from Super PI 1.9 page.
He multiplied this number by 113 and obtained 355. From this he deduced that of the traditional values of π , that is 3, 3.14, 22 / 7 and 355 / 113 , the last is the most exact. [ 2 ]
The number π (/ p aɪ / ⓘ; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, ... Fractions such as 22 / 7 and 355 / 113 ...
In 1585 Anthonisz discovered that the ratio of a circle's circumference to its diameter, later called pi, approximated the fractional value of 355 / 113 .His son Adriaan Metius later published his father's results, and the value 355 / 113 is traditionally referred to as Metius' number'.
Proofs of the mathematical result that the rational number 22 / 7 is greater than π (pi) date back to antiquity. One of these proofs, more recently developed but requiring only elementary techniques from calculus, has attracted attention in modern mathematics due to its mathematical elegance and its connections to the theory of Diophantine approximations.
Jacob de Gelder's 355/113 construction Ramanujan's 355/113 construction Jacob de Gelder published in 1849 a construction based on the approximation π ≈ 355 113 = 3.141 592 920 … {\displaystyle \pi \approx {\frac {355}{113}}=3.141\;592{\color {red}\;920\;\ldots }} This value is accurate to six decimal places and has been known in China ...
Lazzarini's "experiment" is an example of confirmation bias, as it was set up to replicate the already well-known approximation of 355 / 113 (in fact, there is no better rational approximation with fewer than five digits in the numerator and denominator, see also Milü), yielding a more accurate "prediction" of π than would be expected ...