In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from...

A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a reflective surface used to collect or project energy such as light, sound...

there are two distinct lines that lie on the surface. The hyperbolic paraboloid and the hyperboloid of one sheet are doubly ruled surfaces. The plane...

surfaces in the Euclidean space are second order surfaces, the hyperbolic paraboloid z = x 2 − y 2 {\displaystyle z=x^{2}-y^{2}} (which is often referred to...

paraboloid domes have circular bases and horizontal sections and are a type of "circular dome" for that reason. Because of their shape, paraboloid domes...

inscribed paraboloid. Therefore, the volume of the flipped paraboloid is equal to the volume of the cylinder part outside the inscribed paraboloid. In other...

surface dimpled in the w direction according to the equation (Flamm's paraboloid) w = 2 r s ( r − r s ) . {\displaystyle w=2{\sqrt {r_{\mathrm {s} }\left(r-r_{\mathrm...

Gallery of hyperbolic paraboloid structures A hyperbolic paraboloid saddle roof: Church Army Chapel, Blackheath A hyperbolic paraboloid saddle roof: The Scotiabank...

which have concave surfaces that are segments of axially symmetrical paraboloids. Usually, the objects are made of glass. The furnace makes use of the...

are easier to manufacture than mirrors with a surface described by a paraboloid or ellipsoid. They suffer from spherical aberration and coma, but do not...

contain circles except parabolic and hyperbolic cylinders and hyperbolic paraboloids. If a quadric contains a circle, then every intersection of the quadric...

Hyperboloid of one sheet Hyperboloid of two sheets Hyperbolic paraboloid (a ruled surface) Paraboloid Dini's surface Pseudosphere Cayley cubic Barth sextic Clebsch...

hyperbolic paraboloid is a doubly ruled surface so it may be used to construct a saddle roof from straight beams. The hyperbolic paraboloid is a doubly...

about the symmetry axis of the parabolae produces a set of confocal paraboloids, the coordinate system of tridimensional parabolic coordinates. Expressed...

free surface will assume a parabolic surface of revolution known as a paraboloid. The free surface at each point is at a right angle to the force acting...

is the basis for the use of this kind of reflector for solar cooking. Paraboloids are compound curves, which are more difficult to make with simple equipment...

Join the paraboloids y = xz and x = yz. The result is shown in Figure 1. The paraboloid y = x z is shown in blue and orange. The paraboloid x = y z is...

A paraboloid, the graph of squared Euclidean distance from the origin...

paraboloid. Using this shape, the stresses of snow as it ages and compresses are less likely to cause it to buckle because in an inverted paraboloid or...

cross section) and c 2 {\displaystyle c_{2}} is a line. The elliptic paraboloid z = x 2 + y 2 {\displaystyle \;z=x^{2}+y^{2}\;} can be generated by  ...

icosahedron cones and cylinders the sphere other quadrics: spheroid, ellipsoid, paraboloid and hyperboloids. Plane vs Solid Geometry Advanced topics include: projective...

problems with multiple constraints using a similar argument. Consider a paraboloid subject to two line constraints that intersect at a single point. As the...

elliptical paraboloid, hyperbolic paraboloid, hyperboloid of one sheet, hyperboloid of two sheets. Elliptic cone Parabolic cylinder Elliptic paraboloid Hyperbolic...

of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution...

because he only needed the fourth power to calculate the volume of the paraboloid he was interested in). He used his result on sums of integral powers to...

called degenerate quadrics) and five non-degenerate quadrics (ellipsoid, paraboloids and hyperboloids), which are detailed in the following tables. The eight...

Newton noted that the free surface of a rotating liquid forms a circular paraboloid and can therefore be used as a telescope, but he could not build one because...

his name, obtained formulas for the volumes of surfaces of revolution (paraboloid, ellipsoid, hyperboloid), and an ingenious method of exponentiation for...

saddle-shape of Pringles chips is mathematically known as a hyperbolic paraboloid. However, Baur could not figure out how to make the chips palatable, and...

and so on to n dimensions. A quadric, such as a hypersphere, ellipsoid, paraboloid, or hyperboloid, is a generalization of a conic section to higher dimensions...