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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 .
He also gave two other approximations of π: π ≈ 22 ⁄ 7 and π ≈ 355 ⁄ 113, which are not as accurate as his decimal result. The latter fraction is the best possible rational approximation of π using fewer than five decimal digits in the numerator and denominator.
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'.
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 since the 5th century as Milü , and in ...
Liu Hui's method of calculating the area of a circle. Liu Hui's π algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of the state of Cao Wei.Before his time, the ratio of the circumference of a circle to its diameter was often taken experimentally as three in China, while Zhang Heng (78–139) rendered it as 3.1724 (from the proportion of the celestial circle to the diameter ...
The last entry of the table has 355 ⁄ 113 as one of its best rational approximations; i.e., there is no better approximation among rational numbers with denominator up to 113. The number 355 ⁄ 113 is also an excellent approximation to π , attributed to Chinese mathematician Zu Chongzhi , who named it Milü . [ 5 ]