椭圆双曲面[Elliptic Hyperboloid] - 达人(其实～我是卧底，来自外星) - 5D艺术网

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2005/02/16 | 椭圆双曲面[Elliptic Hyperboloid]
类别(∑〖数学〗) | 评论(0) | 阅读(45) | 发表于 13:28: <APPLET CODE="http://mathworld.wolfram.com/Live.class" CODEBASE="live" ARCHIVE="http://mathworld.wolfram.com/live.jar" ALIGN=MIDDLE WIDTH=300 HEIGHT=300 ALT="Elliptic hyperboloid"> <PARAM NAME="input_file" VALUE="http://mathworld.wolfram.com/ellhyper.m"> <PARAM NAME="input_archive" VALUE="http://mathworld.wolfram.com/zip/ellhyper.zip">
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The elliptic hyperboloid is the generalization of the hyperboloid to three distinct semimajor axes. The elliptic hyperboloid of one sheet is a ruled surface and has Cartesian equation
(1)

and parametric equations
(2)

(3)

(4)

for , or
(5)

(6)

(7)

or
(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); 0

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