Editing Circle (section)

==Limiting case of other figures==
The circle can be viewed as a [[Limiting case (mathematics)|limiting case]] of various other figures:
* The series of [[regular polygon]]s with ''n'' sides has the circle as its limit as ''n'' approaches infinity. This fact was applied by [[Archimedes]] to [[Approximations of π|approximate π]].
* A [[Cartesian oval]] is a set of points such that a [[weighted sum]] of the distances from any of its points to two fixed points (foci) is a constant. An [[ellipse]] is the case in which the weights are equal. A circle is an ellipse with an eccentricity of zero, meaning that the two foci coincide with each other as the centre of the circle. A circle is also a different special case of a Cartesian oval in which one of the weights is zero.
* A [[superellipse]] has an equation of the form <math>\left|\frac{x}{a}\right|^n\! + \left|\frac{y}{b}\right|^n\! = 1</math> for positive ''a'', ''b'', and ''n''. A supercircle has {{nowrap|1=''b'' = ''a''}}. A circle is the special case of a supercircle in which {{nowrap|''n'' {{=}} 2}}.
* A [[Cassini oval]] is a set of points such that the product of the distances from any of its points to two fixed points is a constant. When the two fixed points coincide, a circle results.
* A [[curve of constant width]] is a figure whose width, defined as the perpendicular distance between two distinct parallel lines each intersecting its boundary in a single point, is the same regardless of the direction of those two parallel lines. The circle is the simplest example of this type of figure.