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A particular special case of a Cartesian oval is a limaçon.
As Descartes discovered, Cartesian ovals may be used in lens design.
A circle is also a different special case of a Cartesian oval in which one of the weights is zero.
The caustic formed by spherical aberration in this case may therefore be described as the evolute of a Cartesian oval.
In addition, foci are used to define the Cassini oval and the Cartesian oval.
An aplanatic lens is an aspherical lens, formed as the surface of revolution of a cartesian oval.
A Cartesian oval is the set of points for each of which the weighted sum of the distances to two given foci is a constant.
One method of drawing certain specific Cartesian ovals, already used by Descartes, is analogous to a standard construction of an ellipse by stretched thread.
In geometry, a Cartesian oval, named after René Descartes, is a plane curve, the set of points that have the same linear combination of distances from two fixed points.
In it he described a mechanical means of drawing mathematical curves with a piece of twine, and the properties of ellipses, Cartesian ovals, and related curves with more than two foci.
Additionally, if a spherical wavefront is refracted through a spherical lens, or reflected from a concave spherical surface, the refracted or reflected wavefront takes on the shape of a Cartesian oval.
Early attempts at making aspheric lenses to correct spherical aberration were made by René Descartes in the 1620s, and by Constantijn Huygens in the 1630s; the cross-section of the shape devised by Descartes for this purpose is known as a Cartesian oval.
