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Ellipsoidal Dome
An ellipsoidal dome is a dome (also see geodesic dome), which has a bottom cross-section which is a circle, but has a cupola whose curve is an ellipse. There are two types of ellipsoidal domes: ''prolate ellipsoidal domes'' and ''oblate ellipsoidal domes''. A prolate ellipsoidal dome is derived by rotating an ellipse around the long axis of the ellipse; an oblate ellipsoidal dome is derived by rotating an ellipse around the short axis of the ellipse. Of small note, in reflecting telescopes the mirror is usually elliptical, so has the form of a "hollow" ellipsoidal dome. The Jameh Mosque of Yazd has an ellipsoidal dome. See also * Beehive tomb * Clochán * Cloister vault * Dome * Ellipsoid * Ellipsoidal coordinates * Elliptical dome * Geodesic dome * Geodesics on an ellipsoid * Great ellipse * Onion dome * Spherical cap * Spheroid A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface (mathematics), surface obtained by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dome
A dome () is an architectural element similar to the hollow upper half of a sphere. There is significant overlap with the term cupola, which may also refer to a dome or a structure on top of a dome. The precise definition of a dome has been a matter of controversy and there are a wide variety of forms and specialized terms to describe them. A dome can rest directly upon a Rotunda (architecture), rotunda wall, a Tholobate, drum, or a system of squinches or pendentives used to accommodate the transition in shape from a rectangular or square space to the round or polygonal base of the dome. The dome's apex may be closed or may be open in the form of an Oculus (architecture), oculus, which may itself be covered with a roof lantern and cupola. Domes have a long architectural lineage that extends back into prehistory. Domes were built in ancient Mesopotamia, and they have been found in Persian architecture, Persian, Ancient Greek architecture, Hellenistic, Ancient Roman architecture, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Spheroid
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface (mathematics), surface obtained by Surface of revolution, rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a ''prolate spheroid'', elongated like a rugby ball. The ball (gridiron football), American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an ''oblate spheroid'', flattened like a lentil or a plain M&M's, M&M. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation of the Earth, rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattening, flattened in the direction of its axis of rotation. For that reason, in cartography and geode ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Spherical Cap
In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball (mathematics), ball cut off by a plane (mathematics), plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center (geometry), center of the sphere (forming a great circle), so that the height of the cap is equal to the radius of the sphere, the spherical cap is called a ''Sphere#Hemisphere, hemisphere''. Volume and surface area The volume of the spherical cap and the area of the curved surface may be calculated using combinations of * The radius r of the sphere * The radius a of the base of the cap * The height h of the cap * The Spherical coordinate system, polar angle \theta between the rays from the center of the sphere to the apex of the cap (the pole) and the edge of the disk (mathematics), disk forming the base of the cap. These variables are inter-related through the formulas a = r \sin \theta, h = r ( 1 - \cos \theta ), 2hr = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Onion Dome
An onion dome is a dome whose shape resembles an onion. Such domes are often larger in diameter than the tholobate (drum) upon which they sit, and their height usually exceeds their width. They taper smoothly upwards to a point. It is a typical feature of churches belonging to the Russian Orthodox church. There are similar buildings in other Eastern European countries, and occasionally in Western Europe: Bavaria (Germany), Austria, and northeastern Italy. Buildings with onion domes are also found in the Oriental regions of Central and South Asia, and the Middle East. However, old buildings outside Russia usually lack the construction typical of the Russian onion design. Other types of Eastern Orthodox cupolas include ''helmet domes'' (for example, those of the Dormition Cathedral in Vladimir), Ukrainian ''pear domes'' ( St Sophia Cathedral in Kyiv), and Baroque ''bud domes'' ( St Andrew's Church in Kyiv) or an onion-helmet mixture like the St Sophia Cathedral in Novgorod. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Great Ellipse
150px, A spheroid A great ellipse is an ellipse passing through two points on a spheroid and having the same center as that of the spheroid. Equivalently, it is an ellipse on the surface of a spheroid and centered on the origin, or the curve formed by intersecting the spheroid by a plane through its center. For points that are separated by less than about a quarter of the circumference of the earth, about 10\,000\,\mathrm, the length of the great ellipse connecting the points is close (within one part in 500,000) to the geodesic distance. The great ellipse therefore is sometimes proposed as a suitable route for marine navigation. The great ellipse is special case of an earth section path. Introduction Assume that the spheroid, an ellipsoid of revolution, has an equatorial radius a and polar semi-axis b. Define the flattening f=(a-b)/a, the eccentricity e=\sqrt, and the second eccentricity e'=e/(1-f). Consider two points: A at (geographic) latitude \phi_1 and longitude \l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Geodesics On An Ellipsoid
The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an '' oblate ellipsoid'', a slightly flattened sphere. A ''geodesic'' is the shortest path between two points on a curved surface, analogous to a straight line on a plane surface. The solution of a triangulation network on an ellipsoid is therefore a set of exercises in spheroidal trigonometry . If the Earth is treated as a sphere, the geodesics are great circles (all of which are closed) and the problems reduce to ones in spherical trigonometry. However, showed that the effect of the rotation of the Earth results in its resembling a slightly oblate ellipsoid: in this case, the equator and the meridians are the only simple closed geodesics. Furthermore, the shortest path between two points on the equator does not necessarily run along the equator. Finally, if the ellipsoid is further perturbed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Geodesic Dome
A geodesic dome is a hemispherical thin-shell structure (lattice-shell) based on a geodesic polyhedron. The rigid triangular elements of the dome distribute stress throughout the structure, making geodesic domes able to withstand very heavy loads for their size. History The first geodesic dome was designed after World War I by Walther Bauersfeld, chief engineer of Carl Zeiss Jena, an optical company, for a planetarium to house his planetarium projector. An initial, small dome was patented and constructed by the firm of Dykerhoff and Wydmann on the roof of the Carl Zeiss Werke in Jena, Germany. A larger dome, called "The Wonder of Jena", opened to the public on July 18, 1926. Twenty years later, Buckminster Fuller coined the term "geodesic" from field experiments with artist Kenneth Snelson at Black Mountain College in 1948 and 1949. Although Fuller was not the original inventor, he is credited with the U.S. popularization of the idea for which he received on 29 J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Elliptical Dome
An elliptical dome, or an ''oval dome'', is a dome whose bottom Cross section (geometry), cross-section takes the form of an ellipse. Technically, an ''ellipsoidal dome'' has a circular cross-section, so is not quite the same. While the cupola can take different Geometric shape, geometries, when the ceiling's cross-section takes the form of an ellipse, and due to the reflecting properties of an ellipse, any two persons standing at a Focus (geometry), focus of the floor's ellipse can have one whisper, and the other hears; this is a whispering gallery. The largest elliptical dome in the world is at the Sanctuary of Vicoforte in Vicoforte, Italy. In architecture Elliptical domes have many applications in architecture; and are useful in covering rectangular spaces. The Spheroid#Oblate_spheroids, oblate, or horizontal elliptical dome is useful when there is a need to limit height of the space that would result from a spherical dome. As the mathematical description of an elliptical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Ellipsoidal Coordinates
Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system (\lambda, \mu, \nu) that generalizes the two-dimensional elliptic coordinate system. Unlike most three-dimensional orthogonal coordinate systems that feature quadratic coordinate surfaces, the ellipsoidal coordinate system is based on confocal quadrics. Basic formulae The Cartesian coordinates (x, y, z) can be produced from the ellipsoidal coordinates ( \lambda, \mu, \nu ) by the equations : x^ = \frac : y^ = \frac : z^ = \frac where the following limits apply to the coordinates : - \lambda < c^ < - \mu < b^ < -\nu < a^. Consequently, surfaces of constant are s : whereas surfaces of constant are |
Ellipsoid
An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a Surface (mathematics), surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, an ellipsoid is characterized by either of the two following properties. Every planar Cross section (geometry), cross section is either an ellipse, or is empty, or is reduced to a single point (this explains the name, meaning "ellipse-like"). It is Bounded set, bounded, which means that it may be enclosed in a sufficiently large sphere. An ellipsoid has three pairwise perpendicular Rotational symmetry, axes of symmetry which intersect at a Central symmetry, center of symmetry, called the center of the ellipsoid. The line segments that are delimited on the axes of symmetry by the ellipsoid are called the ''principal ax ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
