# Strophoid

A third-order plane algebraic curve whose equation takes the form

in Cartesian coordinates, and

in polar coordinates. The coordinate origin is a node with tangents (see Fig.). The asymptote is . The area of the loop is

The area between the curve and the asymptote is

A strophoid is related to the so-called cusps (cf. Cusp).

Figure: s090630a

#### References

 [1] A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian) [2] A.S. Smogorzhevskii, E.S. Stolova, "Handbook of the theory of planar curves of the third order" , Moscow (1961) (In Russian)