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In mathematics, a paraboloid is a quadric surface of special kind. There are two kinds of paraboloids: elliptic and hyperbolic. The ''elliptic paraboloid'' is shaped like an oval cup and can have a maximum or minimum point. In a suitable coordinate system with three axes , , and , it can be represented by the equation : where and are constants that dictate the level of curvature in the - and - planes respectively. This is an elliptic paraboloid which opens upward for c>0 and downward for c<0. The ''hyperbolic paraboloid'' (not to be confused with a hyperboloid) is a doubly ruled surface shaped like a saddle. In a suitable coordinate system, a hyperbolic paraboloid can be represented by the equation : For c>0, this is a hyperbolic paraboloid that opens down along the x-axis and up along the y-axis (i.e., the parabola in the plane x=0 opens upward and the parabola in the plane y=0 opens downward). == Properties == With ''a = b'' an elliptic paraboloid is a ''paraboloid of revolution'': a surface obtained by revolving a parabola around its axis. It is the shape of the parabolic reflectors used in mirrors, antenna dishes, and the like; and is also the shape of the surface of a rotating liquid, a principle used in liquid mirror telescopes and in making solid telescope mirrors (see Rotating furnace). This shape is also called a ''circular paraboloid''. There is a point called the ''focus'' (or ''focal point'') on the axis of a circular paraboloid such that, if the paraboloid is a mirror, light from a point source at the focus is reflected into a parallel beam, parallel to the axis of the paraboloid. This also works the other way around: a parallel beam of light incident on the paraboloid parallel to its axis is concentrated at the focal point. This applies also for other waves, hence parabolic antennas. For a geometrical proof, click here. The hyperbolic paraboloid is a doubly ruled surface: it contains two families of mutually skew lines. The lines in each family are parallel to a common plane, but not to each other. 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「paraboloid」の詳細全文を読む スポンサード リンク
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