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2. Pi - Wikipedia

   en.wikipedia.org/wiki/Pi

   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.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.

3. List of formulae involving π - Wikipedia

   en.wikipedia.org/wiki/List_of_formulae_involving_π

   where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.

4. Proof that 22/7 exceeds π - Wikipedia

   en.wikipedia.org/wiki/Proof_that_22/7_exceeds_π

   Julian Havil ends a discussion of continued fraction approximations of π with the result, describing it as "impossible to resist mentioning" in that context. [2] The purpose of the proof is not primarily to convince its readers that ⁠ 22 / 7 ⁠ (or ⁠3 + 1 / 7 ⁠) is indeed bigger than π; systematic methods of computing the value of π ...

5. List of mathematical constants - Wikipedia

   en.wikipedia.org/wiki/List_of_mathematical_constants

   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.

6. Approximations of π - Wikipedia

   en.wikipedia.org/wiki/Approximations_of_π

   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:

7. Leibniz formula for π - Wikipedia

   en.wikipedia.org/wiki/Leibniz_formula_for_π

   In mathematics, the Leibniz formula for π, named after Gottfried Wilhelm Leibniz, states that = + + = = +,. an alternating series.. It is sometimes called the Madhava–Leibniz series as it was first discovered by the Indian mathematician Madhava of Sangamagrama or his followers in the 14th–15th century (see Madhava series), [1] and was later independently rediscovered by James Gregory in ...