A plane curve is a curve that lies in a single plane . A plane curve may be closed or open. Curves which are interesting for some reason
and whose properties have therefore been investigates are called "special"
curves (Lawrence 1972). Some of the most common open curves are the line ,
parabola , and hyperbola ,
and some of the most common closed curves are the circle
and ellipse .
See also Algebraic Curve ,
Curve ,
Lamina ,
Perimeter ,
Space
Curve ,
Spherical Curve Explore this topic in the MathWorld classroom
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References Archibald, R. C. "Curves." Encyclopædia Britannica, 14th ed. Archibald, R. C. "The Cardioide and
Some of Its Related Curves." Inaugural dissertation der Mathematischen und Naturwissenschaftlichen
Facultät der Kaiser-Wilhelms-Universität, Strassburg zur Erlangung der
Doctorwürde. Strassburg, France: J. Singer, 1900. Coolidge,
J. L. A
Treatise on Algebraic Plane Curves. Gray,
A. "Famous Plane Curves." Ch. 3 in Modern
Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Hilbert, D. and Cohn-Vossen,
S. "Plane Curves." §1 in Geometry
and the Imagination. Lawrence,
J. D. A
Catalog of Special Plane Curves. Lockwood,
E. H. A
Book of Curves. MacTutor
History of Mathematics Archive. http://www-groups.dcs.st-and.ac.uk/~history/Curves/Curves.html . Shikin,
E. V. Handbook
and Atlas of Curves. Smith,
D. E. "Certain Well-Known Curves." History
of Mathematics, Vol. 2: Special Topics of Elementary Mathematics. Teixeira, F. G. Traité
des courbes spéciales remarquables plane et gauches, 3 vols. Coimbra,
Portugal, 1908-1915. Reprinted New York: Chelsea, 1971 and Paris: Gabay. Wassenaar,
J. "2-D Curves." http://www.2dcurves.com/ . Yates,
R. C. A
Handbook on Curves and Their Properties. Zwikker, C. The
Advanced Geometry of Plane Curves and Their Applications. Referenced on Wolfram|Alpha Plane Curve
Cite this as:
Weisstein, Eric W. "Plane Curve." From
MathWorld https://mathworld.wolfram.com/PlaneCurve.html
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