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Hyperboloid of one sheet : ウィキペディア英語版
Hyperboloid

In mathematics, a hyperboloid is a quadric – a type of surface in three dimensions – described by the equation
: + - = 1   (hyperboloid of one sheet),
or
: + - = -1   (hyperboloid of two sheets).
Both of these surfaces asymptote to the same conical surface as x or y become large:
: + - = 0
These are also called elliptical hyperboloids. If and only if ''a'' = ''b'', it is a hyperboloid of revolution, and is also called a circular hyperboloid.
== Cartesian coordinates ==

Cartesian coordinates for the hyperboloids can be defined, similar to spherical coordinates, keeping the azimuth angle , but changing inclination ''v'' into hyperbolic trigonometric functions:
One-surface hyperboloid:
:x=a \cosh v \cos\theta
:y=b \cosh v \sin\theta
:z=c \sinh v
Two-surface hyperboloid:
:x=a \sinh v \cos\theta
:y=b \sinh v \sin\theta
:z=\pm c \cosh v

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Hyperboloid」の詳細全文を読む



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