A plane algebraic curve of order 4; a conchoid of a circle of diameter (see Fig.).
The equation in rectangular coordinates is
in polar coordinates it is
The coordinate origin is a double point, which is an isolated point for , a node for , and a cusp for (in this case Pascal's limaçon is a cardioid). The arc length can be expressed by an elliptic integral of the second kind. The area bounded by Pascal's limaçon is
The limaçon is named after E. Pascal, who first treated it in the first half of the 17th century.
|||A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)|
E. Pascal is the father of B. Pascal, the famous one.
|[a1]||M. Berger, "Geometry" , 1–2 , Springer (1987) (Translated from French)|
|[a2]||F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971)|
|[a3]||J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972) pp. 113–118|
Pascal limaçon. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pascal_lima%C3%A7on&oldid=12704