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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.
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]
[10] [12] [16] π is also the smallest positive number at which the sine function equals zero, and the difference between consecutive zeroes of the sine function. The cosine and sine can be defined independently of geometry as a power series, [17] or as the solution of a differential equation. [16]
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
In mathematics, Machin-like formulas are a popular technique for computing π (the ratio of the circumference to the diameter of a circle) to a large number of digits.They are generalizations of John Machin's formula from 1706:
The constant π (pi) has a natural definition in Euclidean geometry as the ratio between the circumference and diameter of a circle. It may be found in many other places in mathematics: for example, the Gaussian integral, the complex roots of unity, and Cauchy distributions in probability. However, its ubiquity is not limited to pure mathematics.
IBM System/4 Pi, a family of avionics computers 4Pi microscope , a microscope that uses interference and fluorescence computers 4×π = 12.56637..., the solid angle of a complete sphere measured in steradians
1.5 × 10 −4 [33] = (/) sine-square weak mixing angle: 0.223 05 (23) [g] 0.231 21 (4) [h] 0.231 53 (4) [i] 1.0 × 10 −3 1.7 × 10 −4 1.7 × 10 −4 [34] [35] [35] electron g-factor: −2.002 319 304 360 92 (36) 1.8 × 10 −13 [36]
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