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A hyperbolic paraboloid with lines contained in it Pringles fried snacks are in the shape of a hyperbolic paraboloid. 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. Hence the hyperbolic paraboloid is a conoid.
Strictly, the three-dimensional shape of the reflector is called a paraboloid. A parabola is the two-dimensional figure. (The distinction is like that between a sphere and a circle.) However, in informal language, the word parabola and its associated adjective parabolic are often used in place of paraboloid and paraboloidal. [2]
Paraboloidal coordinates are three-dimensional orthogonal coordinates (,,) that generalize two-dimensional parabolic coordinates.They possess elliptic paraboloids as one-coordinate surfaces.
The red paraboloid corresponds to τ=2, the blue paraboloid corresponds to σ=1, and the yellow half-plane corresponds to φ=-60°. The three surfaces intersect at the point P (shown as a black sphere) with Cartesian coordinates roughly (1.0, -1.732, 1.5).
The fact that the volume of any pyramid, regardless of the shape of the base, including cones (circular base), is (1/3) × base × height, can be established by Cavalieri's principle if one knows only that it is true in one case. One may initially establish it in a single case by partitioning the interior of a triangular prism into three ...
Solid paraboloid of revolution around z-axis: a = the radius of the base circle h = the height of the paboloid from the base cicle's center to the edge Solid ellipsoid: a, b, c = the principal semi-axes of the ellipsoid
The hyperbolic volume of the figure-eight knot is 2.0298832. In the mathematical field of knot theory, the hyperbolic volume of a hyperbolic link is the volume of the link's complement with respect to its complete hyperbolic metric. The volume is necessarily a finite real number, and is a topological invariant of the link. [1]
The cylinder is spun until it reaches a few revolutions per minute. The liquid gradually forms a paraboloid, the shape of a conventional telescopic mirror. The mirror's surface is very precise, and small imperfections in the cylinder's shape do not affect it. The amount of mercury used is small, less than a millimeter in thickness.