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...
15 KB (2,335 words) - 22:25, 1 April 2024
Parabolic reflector (redirect from Paraboloid reflector)
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...
21 KB (2,638 words) - 04:44, 7 October 2024
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...
9 KB (1,010 words) - 13:20, 17 August 2024
Dome (redirect from Paraboloid dome)
paraboloid domes have circular bases and horizontal sections and are a type of "circular dome" for that reason. Because of their shape, paraboloid domes...
175 KB (20,798 words) - 17:15, 16 September 2024
Schwarzschild metric (redirect from Flamm's paraboloid)
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...
38 KB (5,056 words) - 22:30, 11 September 2024
Cavalieri's principle (section Paraboloids)
inscribed paraboloid. Therefore, the volume of the flipped paraboloid is equal to the volume of the cylinder part outside the inscribed paraboloid. In other...
14 KB (1,839 words) - 19:35, 10 October 2024
Gallery of hyperbolic paraboloid structures A hyperbolic paraboloid saddle roof: Church Army Chapel, Blackheath A hyperbolic paraboloid saddle roof: The Scotiabank...
3 KB (307 words) - 07:11, 29 April 2024
Ruled surface (section Hyperbolic paraboloid)
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...
18 KB (2,884 words) - 21:58, 2 October 2024
Circular section (section Elliptical paraboloid)
contain circles except parabolic and hyperbolic cylinders and hyperbolic paraboloids. If a quadric contains a circle, then every intersection of the quadric...
12 KB (2,631 words) - 18:20, 14 March 2024
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...
33 KB (1,055 words) - 03:37, 15 September 2024
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...
15 KB (1,870 words) - 02:12, 5 May 2024
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...
30 KB (4,030 words) - 11:14, 3 October 2024
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...
21 KB (2,725 words) - 20:15, 11 September 2024
which have concave surfaces that are segments of axially symmetrical paraboloids. Usually, the objects are made of glass. The furnace makes use of the...
5 KB (682 words) - 20:58, 17 September 2024
A paraboloid, the graph of squared Euclidean distance from the origin...
25 KB (3,187 words) - 10:11, 23 August 2024
Moses Lake Public Library, showing its distinctive hyperbolic-paraboloid roof...
33 KB (3,230 words) - 20:06, 31 August 2024
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...
2 KB (182 words) - 20:29, 29 July 2023
about the symmetry axis of the parabolae produces a set of confocal paraboloids, the coordinate system of tridimensional parabolic coordinates. Expressed...
8 KB (1,109 words) - 11:44, 7 June 2024
problems with multiple constraints using a similar argument. Consider a paraboloid subject to two line constraints that intersect at a single point. As the...
50 KB (7,780 words) - 05:43, 11 September 2024
the paraboloid M = {(x, y, z) : z = x2 + y2}, with the metric g being the ordinary Euclidean distance coming from the embedding of the paraboloid in Euclidean...
8 KB (943 words) - 17:59, 19 September 2024
icosahedron cones and cylinders the sphere other quadrics: spheroid, ellipsoid, paraboloid and hyperboloids. Advanced topics include: projective geometry of three...
9 KB (375 words) - 17:33, 22 September 2024
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...
135 KB (15,027 words) - 02:17, 25 September 2024
Hyperboloid of one sheet Hyperboloid of two sheets Hyperbolic paraboloid (a ruled surface) Paraboloid Dini's surface Pseudosphere Cayley cubic Barth sextic Clebsch...
2 KB (169 words) - 08:26, 29 April 2024
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...
87 KB (9,766 words) - 15:22, 8 October 2024
terraces, which has now been demolished, was formed from eight hyperbolic-paraboloid umbrellas each approximately 30 square feet (2.8 m2), designed by T. H...
13 KB (828 words) - 10:26, 29 September 2024
called degenerate quadrics) and five non-degenerate quadrics (ellipsoid, paraboloids and hyperboloids), which are detailed in the following tables. The eight...
41 KB (7,405 words) - 16:10, 6 June 2024
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...
33 KB (3,057 words) - 03:14, 27 September 2024
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...
15 KB (2,751 words) - 18:50, 24 January 2024
his name, obtained formulas for the volumes of surfaces of revolution (paraboloid, ellipsoid, hyperboloid), and an ingenious method of exponentiation for...
139 KB (16,144 words) - 23:36, 9 October 2024
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...
7 KB (859 words) - 23:06, 26 August 2024