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The number π (/ p aɪ /; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159.The number π appears in many formulae across mathematics and physics.
Although it is not a book on fractions, the meaning, nature, and four operations of fractions are fully discussed. For example: combined division (addition), subtraction (subtraction), multiplication (multiplication), warp division (division), division (comparison size), reduction (simplified fraction), and bisector (average). [9]
Hence Mikami strongly urged that the fraction 355 / 113 be named after Zu Chongzhi as Zu's fraction. [7] In Chinese literature, this fraction is known as "Zu's ratio". Zu's ratio is a best rational approximation to π, and is the closest rational approximation to π from all fractions with denominator less than 16600. [8]
Piphilology comprises the creation and use of mnemonic techniques to remember many digits of the mathematical constant π.The word is a play on the word "pi" itself and of the linguistic field of philology.
Thus all three corresponding sides are in the same proportion; in particular, we have C′A : C′C = C′P : C′A and AP : C′A = CA : C′C. The center of the circle, O, bisects A′A, so we also have triangle OAP similar to A′AB, with OP half the length of A′B. In terms of side lengths, this gives us
S n is the approximation after taking n terms. Each subsequent subplot magnifies the shaded area horizontally by 10 times. (click for detail) He used the first 21 terms to compute an approximation of π correct to 11 decimal places as 3.141 592 653 59. He also improved the formula based on arctan(1) by including a correction:
The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one.
The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant pi (π).For more detailed explanations for some of these calculations, see Approximations of π.
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