Circumference

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The circumference is the distance around a closed curve. Circumference is a kind of perimeter.

Circle

The circumference of a circle can be calculated from its diameter using the formula:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c = \pi d}

Or, substituting the radius for the diameter:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c = 2r\pi}

Where r is the radius and d is the diameter of the circle, and π (the Greek letter pi) is the constant 3.141 592 6...

Ellipse

The circumference of an ellipse is more problematical, the exact solution being an infinite series. A good approximation is Ramanujan's:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c \approx \pi (3(a+b) - \sqrt{(3a+b)(a+3b)})}

where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} are the ellipse's semi-major and semi-minor axes, respectively. The two are related by the ellipse's eccentricity as follows:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b = a \sqrt{1-e^2}}

Which means the circumference can also be written as:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c \approx \pi a (3(1+\sqrt{1-e^2}) - \sqrt{(3+ \sqrt{1-e^2})(1+3 \sqrt{1-e^2})}) = \pi a (3(1+\sqrt{1-e^2}) - \sqrt{3(2-e^2)+10 \sqrt{1-e^2}})}

External link

bg:Обиколка de:Umfang et:Ümbermõõt es:Circunferencia fr:Circonférence it:Circonferenza nl:Omtrek nn:Omkrins ja:円周 pl:Obwód sr:Обим (геометрија) th:เส้นรอบวง zh:周长