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

单词

Elliptic Hyperboloid

释义

Elliptic Hyperboloid

The elliptic hyperboloid is the generalization of the Hyperboloid to three distinct semimajor axes. Theelliptic hyperboloid of one sheet is a Ruled Surface and has Cartesian equation

(1)

and parametric equations

			(2)
			(3)
			(4)

for

, or

			(5)
			(6)
			(7)

			(8)
			(9)
			(10)

The two-sheeted elliptic hyperboloid oriented along the z-Axis has Cartesian equation

(11)

and parametric equations

			(12)
			(13)
			(14)

The two-sheeted elliptic hyperboloid oriented along the x-Axis has Cartesian equation

(15)

and parametric equations

			(16)
			(17)
			(18)

See also Hyperboloid, Ruled Surface

References

Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 296-297, 1993.

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