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Plane Curve

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PlaneCurves

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. New York: Dover, p. 30, 1959.Gray, A. "Famous Plane Curves." Ch. 3 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 49-74, 1997.Hilbert, D. and Cohn-Vossen, S. "Plane Curves." §1 in Geometry and the Imagination. New York: Chelsea, pp. 1-7, 1999.Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, 1972.Lockwood, E. H. A Book of Curves. Cambridge, England: Cambridge University Press, 1961.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. Boca Raton, FL: CRC Press, 1995.Smith, D. E. "Certain Well-Known Curves." History of Mathematics, Vol. 2: Special Topics of Elementary Mathematics. New York: Dover, pp. 326-331, 1958.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. Ann Arbor, MI: J. W. Edwards, 1947.Zwikker, C. The Advanced Geometry of Plane Curves and Their Applications. New York: Dover, 1963.

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Plane Curve

Cite this as:

Weisstein, Eric W. "Plane Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PlaneCurve.html

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