Curve
In topology, a curve is a one-dimensional continuum
(Charatonik and Prajs 2001).
In analytic geometry, a curve is continuous map from a one-dimensional space to
an 
-dimensional space. Loosely
speaking, the word "curve" is often used to mean the function
graph of a two- or three-dimensional curve. The simplest curves can be represented
parametrically in 
-dimensional space
as
Other simple curves can be simply defined only implicitly, i.e., in the form
 |
(5)
|
SEE ALSO: Continuum,
Plane Curve,
Space Curve,
Spherical
Curve
Portions of this entry contributed by Matt
Insall (author's link)
REFERENCES:
Charatonik, J. J. and Prajs, J. R. "On Local Connectedness of Absolute
Retracts." Pacific J. Math. 201, 83-88, 2001.
Cundy, H. and Rollett, A. Mathematical
Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 71-75, 1989.
"Geometry." The New Encyclopædia Britannica, 15th ed. 19,
pp. 946-951, 1990.
Gallier, J. H. Curves and Surfaces for Geometric Design: Theory and Algorithms. New York: Academic
Press, 1999.
Oakley, C. O. Analytic
Geometry. New York: Barnes and Noble, 1957.
Rutter, J. W. Geometry
of Curves. Boca Raton, FL: Chapman and Hall/CRC, 2000.
Shikin, E. V. Handbook
and Atlas of Curves. Boca Raton, FL: CRC Press, 1995.
Seggern, D. von CRC
Standard Curves and Surfaces. Boca Raton, FL: CRC Press, 1993.
Smith, P. F.; Gale, A. S.; and Neelley, J. H. New
Analytic Geometry, Alternate Edition. Boston, MA: Ginn and Company, 1938.
Walker, R. J. Algebraic
Curves. New York: Springer-Verlag, 1978.
Weisstein, E. W. "Books about Curves." http://www.ericweisstein.com/encyclopedias/books/Curves.html.
Yates, R. C. The Trisection Problem. Reston, VA: National Council of Teachers of Mathematics,
1971.
Zwikker, C. The Advanced Geometry of Plane Curves and Their Applications. New York: Dover,
1963.
Zwillinger, D. (Ed.). "Algebraic Curves." §8.1 in CRC Standard Mathematical Tables and Formulae, 3rd ed. Boca Raton, FL: CRC Press,
1996.
Referenced on Wolfram|Alpha:
Curve
CITE THIS AS:
Insall, Matt and Weisstein, Eric W. "Curve." From MathWorld--A Wolfram
Web Resource. http://mathworld.wolfram.com/Curve.html
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