An elliptic paraboloid is a type of quadric surface that is defined by a quadratic equation in three variables. It is a doubly ruled surface, meaning that it can be generated by two families of straight lines that intersect each other. The surface is shaped like a bowl or a saddle, with a central point called the vertex. The vertex is the lowest point on the surface and is located at the origin of the coordinate system. The elliptic paraboloid is the three-dimensional analog of an elliptic cone, and it can be generated by rotating an ellipse around its minor axis. Elliptic paraboloids have a variety of applications in mathematics, physics, engineering, and architecture. In mathematics, they are used to model surfaces of revolution and to study partial differential equations. In physics, they are used to model the shape of reflectors and antennas. In engineering, they are used to design buildings, bridges, and other structures that require curved surfaces. In architecture, they are used to create interesting and unique shapes for buildings and other structures. One important property of elliptic paraboloids is that they have a constant curvature along their ruling lines. This means that the surface is smooth and has no sharp edges or corners. Another important property is that the surface is symmetric about its vertex. This means that any point on the surface can be reflected across the vertex to obtain another point on the surface. In conclusion, an elliptic paraboloid is a type of quadric surface that is defined by a quadratic equation in three variables. It is a doubly ruled surface that can be generated by two families of straight lines. The surface is shaped like a bowl or a saddle and has a central point called the vertex. Elliptic paraboloids have a variety of applications in mathematics, physics, engineering, and architecture, and they have important properties such as constant curvature along their ruling lines and symmetry about their vertex.
quadric surface, doubly ruled surface, curvature, symmetry, reflectors
CITATION : "Christopher White. 'Elliptic Paraboloid.' Design+Encyclopedia. https://design-encyclopedia.com/?E=360671 (Accessed on July 06, 2025)"
An elliptic paraboloid is a type of surface that is defined by a quadratic equation in three variables. It is a doubly ruled surface, meaning that it can be generated by two families of straight lines. It is the three-dimensional analog of an elliptic cone, and is a member of the family of quadric surfaces. It is the surface of revolution obtained by rotating an ellipse around its minor axis. It can be seen as the surface generated by the intersection of a cylinder and an elliptic cone. It can also be seen as the surface of revolution generated by rotating an ellipse around its minor axis. Elliptic paraboloids have a variety of applications in mathematics, physics, engineering, and architecture.
Ellipse, paraboloid, cylinder, revolution, quadric surfaces.
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