Pi
The number π is a mathematical constant. It is defined as the ratio of a circle’s circumference to its diameter. Being an irrational number, π cannot be expressed as a common fraction. Adepts have succeeded in memorizing the value of π to over 70,000 digits.
About Pi in brief
The number π is a mathematical constant. It is defined as the ratio of a circle’s circumference to its diameter. It appears in many formulas in all areas of mathematics and physics. Being an irrational number, π cannot be expressed as a common fraction. Its decimal representation never ends and never settles into a permanently repeating pattern. Adepts have succeeded in memorizing the value of π to over 70,000 digits. The extensive calculations involved have also been used to test supercomputers and high-precision multiplication algorithms. The symbol used by mathematicians to represent the ratio is the lowercase Greek letter π, sometimes spelled out as pi, and derived from the first letter of the Greek word perimetros, meaning circumference. The choice of the symbol was discussed in the section Adoption of the Symbol π. For example, one may directly compute π as an integral: y2 = 1, x2 + 1, as the integral of the equation y x2 – x2. An such as this was adopted as the definition of the π integral in 1841 by Karl Weierstrass, who defined it directly as an Integral.
Here these new definitions will implicitly no longer satisfy the flat formula π = Cd, which is the circumference of a circles arc around the perimeter of the circle. Here, the definition is the arc length of the top half of the unit circle, given in Cartesian coordinates by the coordinates of y x 2 + x2, as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 61, 63, 64, 69, 70, 68, 73, 74, 78, 79, 80, 81, 82, 83, 84, 84 and 83, 86, 87, 88, 89, 90, 90,. 88, 88,. 89, 91, 92, 93, 94, 89,. 90, 92,. 92, 94,. 93, 93,. 94, 95, 96, 97, 98, 99, 100, 102, 103, 104, 104,. 104, 105, 106, 107, 108, 109, 110, 112, 113, 114, 111, 116, 113,. 114, 116,. 116, 117, 118, 119, 123, 118,. 118, 123,. 119, 120, 119,. 122, 123. 123, 124, 130, 124,. 123, 130,. 124, 125, 126, 128, 129, 131, 130.
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This page is based on the article Pi published in Wikipedia (as of Nov. 21, 2020) and was automatically summarized using artificial intelligence.
