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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.
kilogram per cubic meter (kg/m 3) diameter: meter (m) distance: meter (m) direction: unitless impact parameter meter (m) differential (e.g. ) varied depending on context differential vector element of surface area A, with infinitesimally small magnitude and direction normal to surface S
3.14159 26535 89793 23846 [Mw 1] [OEIS 1] Ratio of a circle's circumference to its diameter. 1900 to 1600 BCE [2] Tau: 6.28318 53071 79586 47692 [3] [OEIS 2] Ratio of a circle's circumference to its radius. Equal to : 1900 to 1600 BCE [2] Square root of 2, Pythagoras constant [4]
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.
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 quantity 206 265 ″ is approximately equal to the number of arcseconds in a circle (1 296 000 ″), divided by 2π, or, the number of arcseconds in 1 radian. The exact formula is = (″) and the above approximation follows when tan X is replaced by X.
Euler's identity asserts that is equal to −1. The expression e i π {\displaystyle e^{i\pi }} is a special case of the expression e z {\displaystyle e^{z}} , where z is any complex number . In general, e z {\displaystyle e^{z}} is defined for complex z by extending one of the definitions of the exponential function from real exponents to ...
Here, the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159. One method of deriving this formula, which originated with Archimedes , involves viewing the circle as the limit of a sequence of regular polygons with an increasing number of sides.