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A curve which is invariant under inversion. Examples include the cardioid, cartesian ovals, Cassini ovals, Limaçon, strophoid, and Maclaurin trisectrix.

Taking the origin as the inversion center, Archimedes' spiral r=atheta inverts to the hyperbolic spiral r=a/theta.

If the cusp of the cardioid is taken as the inversion center, the cardioid inverts to a parabola.

If the cusp of the cissoid of Diocles is taken as the inversion center, then the cissoid inverts to a parabola.

A complex map is a map f:C->C. The following table lists several common types of complex maps. map formula domain complex magnification f(z)=az a in R, a>0 complex rotation ...

The inverse curve of Fermat's spiral with the origin taken as the inversion center is the lituus.

Taking the pole as the inversion center, the hyperbolic spiral inverts to Archimedes' spiral r=atheta.

A double rhomboid linkage which gives rectilinear motion from circular without an inversion.

The inverse curve of the Maclaurin trisectrix with inversion center at the negative x-intercept is a Tschirnhausen cubic.

A scalar which reverses sign under inversion is called a pseudoscalar. For example, the scalar triple product A·(BxC) is a pseudoscalar since A·(BxC)=-[-A·((-B)x(-C))].