Circumference

The circumference is the distance around a closed curve.

Circles

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

<math>c = \pi d<math>

Or, substituting the radius for the diameter:

<math>c = 2 \pi r<math>

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...

Ellipses

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

<math>c \approx \pi (3(a+b) - \sqrt{(3a+b)(a+3b)})<math>

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

<math>b = a \sqrt{1-e^2}<math>

Which means the circumference can also be written as:

<math>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}})<math>

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