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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.The number π appears in many formulae across mathematics and physics.
US hat size is the circumference of the head, measured in inches, divided by pi, rounded to the nearest 1/8 inch. This corresponds to the 1D mean diameter. [1] Diameter at breast height is the circumference of tree trunk, measured at height of 4.5 feet, divided by pi. This corresponds to the 1D mean diameter.
The ratio of a circle's circumference to its diameter is π (pi), an irrational constant approximately equal to 3.141592654. The ratio of a circle's circumference to its radius is 2 π . [ a ] Thus the circumference C is related to the radius r and diameter d by: C = 2 π r = π d . {\displaystyle C=2\pi r=\pi d.}
The ratio of the circumference of any circle to its diameter is greater than but less than . This approximates what we now call the mathematical constant π . He found these bounds on the value of π by inscribing and circumscribing a circle with two similar 96-sided regular polygons .
The circumference of a circle is the distance around it, but if, as in many elementary treatments, distance is defined in terms of straight lines, this cannot be used as a definition. Under these circumstances, the circumference of a circle may be defined as the limit of the perimeters of inscribed regular polygons as the number of sides ...
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. = where A is the area of a circle. More generally, =
Let A′ be the point opposite A on the circle, so that A′A is a diameter, and A′AB is an inscribed triangle on a diameter. By Thales' theorem , this is a right triangle with right angle at B. Let the length of A′B be c n , which we call the complement of s n ; thus c n 2 + s n 2 = (2 r ) 2 .
Originally in 1945, the divisions were based on the ring inside diameter in steps of 1 ⁄ 64 inch (0.40 mm). [6] However, in 1987 BSI updated the standard to the metric system so that one alphabetical size division equals 1.25 mm of circumferential length. For a baseline, ring size C has a circumference of 40 mm. [7]
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