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The first few convergents (3, 22/7, 333/106, 355/113, ...) are among the best-known and most widely used historical approximations of π. Sequences of constants [ edit ]
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.
3.125: 1 Between 1 BC and AD 5: Liu Xin [7] [11] [12] Unknown method giving a figure for a jialiang which implies a value for π ≈ 162 ⁄ (√ 50 +0.095) 2. 3.1547... 1 AD 130: Zhang Heng (Book of the Later Han) [2] √ 10 = 3.162277... 736 ⁄ 232: 3.1622... 1 150: Ptolemy [2] 377 ⁄ 120: 3.141666... 3: 250: Wang Fan [2] 142 ⁄ 45: 3 ...
where H is the hypervolume of a 3-sphere and r is the radius. S V = 2 π 2 r 3 {\displaystyle SV=2\pi ^{2}r^{3}} where SV is the surface volume of a 3-sphere and r is the radius.
Illustration of a unit circle. The variable t is an angle measure. Animation of the act of unrolling the circumference of a unit circle, a circle with radius of 1. Since C = 2πr, the circumference of a unit circle is 2π.
Its first few decimal digits are 3.141592653589793... [3] Pi is defined as the ratio of a circle's circumference to its diameter: [4] =. Or, equivalently, as the ratio of the circumference to twice the radius.
The "6 theorem" states that Dehn filling along slopes of length greater than 6 results in a hyperbolike 3-manifold, i.e. an irreducible, atoroidal, non-Seifert-fibered 3-manifold with infinite word hyperbolic fundamental group. Yet again assuming the geometrization conjecture, these manifolds have a complete hyperbolic metric. An argument of ...
In mathematics, Euler's identity [note 1] (also known as Euler's equation) is the equality + = where . is Euler's number, the base of natural logarithms, is the imaginary unit, which by definition satisfies =, and