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The number π (/ p aɪ /; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159.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.
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.
Square root of 3, Theodorus' constant [6] 1.73205 08075 68877 29352 ... 46 to 120 CE [11] Cube root of 3 1.44224 95703 07408 38232 ...
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.
On March 12, 2009, the U.S. House of Representatives passed a non-binding resolution (111 H. Res. 224), [4] recognizing March 14, 2009, as National Pi Day. [11] For Pi Day 2010, Google presented a Google Doodle celebrating the holiday, with the word Google laid over images of circles and pi symbols; [ 12 ] and for the 30th anniversary in 2018 ...
The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1) 2 = x 2 ...
The moment of inertia of a magic square has been defined as the sum over all cells of the number in the cell times the squared ... 11: 5: 8: 10 2: 16: 13: 3 14: 4: 1 ...