Circumference
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Circumference of a circle
The circumference of a circle is the distance around it. The term is used when measuring physical objects, as well as when considering abstract geometric forms.
Relationship with Pi
The circumference of a circle relates to one of the most important mathematical constants in all of mathematics. This constant, pi, is represented by the Greek letter π. The numerical value of π is 3.14159 26535 89793 ... (see OEIS: A000796). 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. The constant ratio of circumference to radius also has many uses in mathematics, engineering, and science. These uses include but are not limited to radians, computer programming, and physical constants. The Greek letter 𝜏 (tau) is sometimes used to represent this constant, but is not generally accepted as proper notation.
Circumference of an ellipse
The circumference of an ellipse can be expressed in terms of the complete elliptic integral of the second kind.
Circumference of a graph
In graph theory the circumference of a graph refers to the longest cycle contained in that graph.
See also
References
External links
- Numericana - Circumference of an ellipse
- Circumference of a circle With interactive applet and animation