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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.
3 mm scale, also known as 3 mm finescale, is a model railway scale of 3 mm : 1 ft (305 mm) used for British prototypes. Introduced as British TT gauge , it sits approximately halfway between British N gauge and OO gauge but is not as popular as either and there is no longer any mass manufacturer ready-to-run support.
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]
Since C = 2πr, the circumference of a unit circle is 2π. In mathematics , a unit circle is a circle of unit radius —that is, a radius of 1. [ 1 ] Frequently, especially in trigonometry , the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane .
2 mm scale, often 2 mm finescale is a specification used for railway modelling, [1] largely for modelling British railway prototypes. [citation needed] It uses a scale of 2 mm on the model to 1 foot on the prototype, which scales out to 1:152. [1] The track gauge used to represent prototype standard gauge (4 feet 8 + 1 ⁄ 2 inches) is 9.42 mm ...
((x),(y) = {239, 13 2} is a solution to the Pell equation x 2 − 2 y 2 = −1.) Formulae of this kind are known as Machin-like formulae . Machin's particular formula was used well into the computer era for calculating record numbers of digits of π , [ 39 ] but more recently other similar formulae have been used as well.
The millimetre (SI symbol: mm) is a unit of length in the metric system equal to 10 −3 metres ( 1 / 1 000 m = 0.001 m). To help compare different orders of magnitude , this section lists lengths between 10 −3 m and 10 −2 m (1 mm and 1 cm).
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: