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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]
Euler's identity is a special case of Euler's formula, which states that for any real number x, = + where the inputs of the trigonometric functions sine and cosine are given in radians. In particular, when x = π, = + . Since
UNESCO's 40th General Conference designated Pi Day as the International Day of Mathematics in November 2019. [ 5 ] [ 6 ] Other dates when people celebrate pi include Pi Approximation Day on July 22 (22/7 in the day/month format, an approximation of π ) and June 28 (6.28, an approximation of 2 π or tau ).
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.
It has been found that a circular area is to the square on a line equal to the quadrant of the circumference, as the area of an equilateral rectangle is to the square on one side. [12] An "equilateral rectangle" is, by definition, a square. This is an assertion that the area of a circle is the same as that of a square with the same perimeter.
((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 , [ 40 ] but more recently other similar formulae have been used as well.
The square root of 2 is equal to the length of the hypotenuse of a right-angled triangle with legs of length 1.. The square root of 2, often known as root 2 or Pythagoras' constant, and written as √ 2, is the unique positive real number that, when multiplied by itself, gives the number 2.