2.2 Circles and ellipses
Acircle is the shape defined by the path of a point moving at a constant distance from another point. The constant distance is termed the 'radius' of the circle. An ellipse is oval in shape, which also comprises a single line which has no ends (ie it joins onto itself) and is defined by a major and minoraxis. Acircleisaspecialcaseofanellipse,wherethelengthsofthetwoaxesareidentical.
The quantity π used in the following formulae is the ratio between the perimeter of a circle and its diameter (the distance from one side of a circle to the other passing through the centre, or twice the value of the radius).
Shape | perimeter | Area | |
Circle (the distances from the centre to the edge of the circle is the same in all directions) |
2 πr | πr^{2} | |
Ellipse (a 'squashed' circle or oval, defined by the lengths of its major and minor axes) |
2π (0.5 . x^{2} . y^{2})^{0.5} (see note below) |
πxy |
Note: the formula for the perimeter of an ellipse is an approximation