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Concept
Circumference
Summary
In geometry, the circumference (from Latin circumferens, meaning "carrying around") is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.
Circumference may also refer to the circle itself, that is, the locus corresponding to the edge of a disk.
The is the circumference, or length, of any one of its great circles.
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 increases without bound. The term circumference is used when measuring physical objects, as well as when considering abstract geometric forms.
The circumference of a circle is related to one of the most important mathematical constants. This constant, pi, is represented by the Greek letter The first few decimal digits of the numerical value of are 3.141592653589793 ... Pi is defined as the ratio of a circle's circumference to its diameter
Or, equivalently, as the ratio of the circumference to twice the radius. The above formula can be rearranged to solve for the circumference:
The ratio of the circle's circumference to its radius is called the circle constant, and is equivalent to . The value is also the amount of radians in one turn. The use of the mathematical constant pi is ubiquitous in mathematics, engineering, and science.
In Measurement of a Circle written circa 250 BCE, Archimedes showed that this ratio ( since he did not use the name pi) was greater than 310/71 but less than 31/7 by calculating the perimeters of an inscribed and a circumscribed regular polygon of 96 sides. This method for approximating pi was used for centuries, obtaining more accuracy by using polygons of larger and larger number of sides.
Official source
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