Paraboloid

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Paraboloid

Definition

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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. 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 up along the x-axis and down 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).