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In geometry, the circumference (from Latin circumferens, meaning "carrying around") is the perimeter of a circle or ellipse. The circumference is the arc length of the circle, as if it were opened up and straightened out to a line segment. [1] More generally, the perimeter is the curve length around any closed figure.
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 .
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 .
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.
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A diameter of an ellipse is any line passing through the centre of the ellipse. [2] Half of any such diameter may be called a semidiameter, although this term is most often a synonym for the radius of a circle or sphere. [3] The longest diameter is called the major axis.
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