Persian curve

spiric curve

A plane algebraic curve of order four that is the line of intersection between the surface of a torus and a plane parallel to its axis (see Fig. a, Fig. b, Fig. c). The equation in rectangular coordinates is

where is the radius of the circle describing the torus, is the distance from the origin to its centre and is the distance from the axis of the torus to the plane. The following are Persian curves: the Booth lemniscate, the Cassini oval and the Bernoulli lemniscate.

Figure: p072400a

.

Figure: p072400b

.

Figure: p072400c

.

The name is after the Ancient Greek geometer Persei (2nd century B.C.), who examined it in relation to research on various ways of specifying curves.

References

[1]	A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)

References

[a1]	F. Gomez Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971)
[a2]	K. Fladt, "Analytische Geometrie spezieller ebener Kurven" , Akad. Verlagsgesell. (1962)