“Serpentine Curve”的概念、定义、习题解题方法及翻译-数学辞典

单词

Serpentine Curve

释义

Serpentine Curve

A curve named and studied by Newton in 1701 and contained in his classification of L'Hospital and Huygens in 1692 (MacTutor Archive).

The curve is given by the Cartesian equation

(1)

and parametric equations

			(2)
			(3)

The curve has a Maximum at and a Minimum at , where

(4)

and inflection points at

, where

(5)

The Curvature is given by

			(6)
			(7)

References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 111-112, 1972.

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

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