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Best rational approximants for π (green circle), e (blue diamond), ϕ (pink oblong), (√3)/2 (grey hexagon), 1/√2 (red octagon) and 1/√3 (orange triangle) calculated from their continued fraction expansions, plotted as slopes y/x with errors from their true values (black dashes)
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.
The Chinese mathematician Liu Hui in 263 CE computed π to between 3.141 024 and 3.142 708 by inscribing a 96-gon and 192-gon; the average of these two values is 3.141 866 (accuracy 9·10 −5). He also suggested that 3.14 was a good enough approximation for practical purposes.
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.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
A History of Pi (book) Indiana Pi Bill; Leibniz formula for pi; Lindemann–Weierstrass theorem (Proof that π is transcendental) List of circle topics; List of formulae involving π; Liu Hui's π algorithm; Mathematical constant (sorted by continued fraction representation) Mathematical constants and functions; Method of exhaustion; Milü; Pi ...
The circumference of a circle with diameter 1 is π.. A mathematical constant is a number whose value is fixed by an unambiguous definition, often referred to by a special symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
In mathematics, at least four different functions are known as the pi or Pi function: ... This page was last edited on 5 October 2024, at 19:28 (UTC).