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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.
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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.
Let be the number of digits to which π is to be calculated. Let be the number of terms in the Taylor series (see equation 2). Let be the amount of time spent on each digit (for each term in the Taylor series). The Taylor series will converge when:
TachusPi by Fabrice Bellard [99] is the program used by himself to compute world record number of digits of pi in 2009. y -cruncher by Alexander Yee [ 47 ] is the program which every world record holder since Shigeru Kondo in 2010 has used to compute world record numbers of digits .
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is the number of collisions made (in ideal conditions, perfectly elastic with no friction) by an object of mass m initially at rest between a fixed wall and another object of mass b 2N m, when struck by the other object. [1]
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