Parabola

The set of all points in the Plane equidistant from a given Line (the Directrix) and a given point not on the line (the Focus).

The parabola was studied by Menaechmus in an attempt to achieve Cube Duplication. Menaechmus solved the problem byfinding the intersection of the two parabolas and . Euclid wrote about the parabola, and it wasgiven its present name by Apollonius. Pascal considered the parabola as a projection of aGalileo showed that projectiles falling under uniform gravity followparabolic paths. Gregory and Newton considered the Catacaustic properties of a parabola whichbring parallel rays of light to a focus (MacTutor Archive).

For a parabola opening to the right, the equation in Cartesian Coordinates is

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

			(9)
			(10)

The Curvature, Arc Length, and Tangential Angle are

			(11)
			(12)
			(13)

The Tangent Vector of the parabola is

			(14)
			(15)

References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 198, 1987.

Casey, J. ``The Parabola.'' Ch. 5 in A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections, Containing an Account of Its Most Recent Extensions, with Numerous Examples, 2nd ed., rev. enl. Dublin: Hodges, Figgis, & Co., pp. 173-200, 1893.

Coxeter, H. S. M. ``Conics.'' §8.4 in Introduction to Geometry, 2nd ed. New York: Wiley, pp. 115-119, 1969.

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 67-72, 1972.

Lee, X. ``Parabola.''http://www.best.com/~xah/SpecialPlaneCurves_dir/Parabola_dir/parabola.html.

Lockwood, E. H. ``The Parabola.'' Ch. 1 in A Book of Curves. Cambridge, England: Cambridge University Press, pp. 2-12, 1967.

MacTutor History of Mathematics Archive. ``Parabola.''http://www-groups.dcs.st-and.ac.uk/~history/Curves/Parabola.html.

Pappas, T. ``The Parabolic Ceiling of the Capitol.'' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 22-23, 1989.

• Poset
• Poset Dimension
• Position Four-Vector
• Position Vector
• Positive
• Positive Definite Function
• Positive Definite Matrix
• Positive Definite Quadratic Form
• Positive Definite Tensor
• Positive Integer
• Positive Semidefinite Matrix
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• Postage Stamp Problem
• Posterior Distribution
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• Potential Function
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• Power
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