Circumference
Circumference
In geometry, the circumference (from Latin circumferentia, meaning "carrying around") of a circle is the (linear) distance around it. That is, the circumference would be the length of the circle if it were opened up and straightened out to a line segment. Since a circle is the edge (boundary) of a disk, circumference is a special case of perimeter. The perimeter is the length around any closed figure and is the term used for most figures excepting the circle and some circular-like figures such as ellipses. Informally, "circumference" may also refer to the edge itself rather than to the length of the edge.
Video: Circumference of a circle
Circumference of a circle
Circle illustration with circumference (C) in black, diameter (D) in cyan, radius (R) in red, and centre or origin (O) in magenta. Circumference = π × diameter = 2 × π × radius.
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 can not 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.[3] The term circumference is used when measuring physical objects, as well as when considering abstract geometric forms.
When a circle's diameter is 1, its circumference is π.
When a circle's radius is 1—called a unit circle—its circumference is 2π.
Relationship with π
The circumference of a circle is related to one of the most important mathematical constants. This constant, pi, is represented by the Greek letter π. The first few decimal digits of the numerical value of π are 3.141592653589793 ...[4] Pi is defined as the ratio of a circle's circumference C to its diameter d:
Or, equivalently, as the ratio of the circumference to twice the radius. The above formula can be rearranged to solve for the circumference:
The use of the mathematical constant π is ubiquitous in mathematics, engineering, and science.
In Measurement of a Circle written circa 250 BCE, Archimedes showed that .......
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