Circumference

The circumference is the distance around a closed curve.

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

c = πd

Or, substituting the radius for the diameter:

c = 2πr

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...

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

$c \approx \pi (3(a+b) - \sqrt{(3a+b)(a+3b)})$

where a and b are the ellipse's semi-major and semi-minor axes, respectively. The two are related by the ellipse's eccentricity as follows:

$b = a \sqrt{1-e^2}$

Which means the circumference can also be written as:

$c \approx \pi a (3(1+\sqrt{1-e^2}) - \sqrt{(3+ \sqrt{1-e^2})(1+3 \sqrt{1-e^2})}) = \pi a (3(1+\sqrt{1-e^2}) - \sqrt{3(2-e^2)+10 \sqrt{1-e^2}})$

External link

Numericana - Circumference of an ellipse (http://home.att.net/~numericana/answer/ellipse.htm#elliptic)

de:Umfang et:Ümbermõõt es:Circunferencia fr:Circonférence it:Circonferenza nl:Omtrek ja:円周 pl:Obwód

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