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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.
At about the same time, the Egyptian Rhind Mathematical Papyrus (dated to the Second Intermediate Period, c. 1600 BCE, although stated to be a copy of an older, Middle Kingdom text) implies an approximation of π as 256 ⁄ 81 ≈ 3.16 (accurate to 0.6 percent) by calculating the area of a circle via approximation with the octagon.
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.
Inscribe a square in the circle, so that its four corners lie on the circle. Between the square and the circle are four segments. If the total area of those gaps, G 4, is greater than E, split each arc in half. This makes the inscribed square into an inscribed octagon, and produces eight segments with a smaller total gap, G 8.
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.
The international standard ISO 216 defines sizes of paper sheets using the √ 2, in which the long side of a rectangular sheet of paper is the square root of two times the short side of the paper. Rectangles in this shape are rep-2. A rectangle (or parallelogram) is rep-n if its aspect ratio is √ n:1.
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