|
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 obtained by rotating an ellipse abou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Spheroid
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by 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 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. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography and geodesy the Earth is often approximated by an oblate spheroid, known as the reference ellipsoid, instead of a sph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Cap
In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the 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 ''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 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 forming the base of the cap If \phi denotes the latitude in geographic coordinates, then \theta+\phi = \pi/2 = 90^\circ\,, and \cos \theta = \sin \phi. The relationship between h and r is relevant as long as 0\le h\le2r. For example, the red section of the illu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Onion Dome
An onion dome is a dome whose shape resembles an onion. Such domes are often larger in diameter than the tholobate upon which they sit, and their height usually exceeds their width. These bulbous structures taper smoothly 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 some Western European countries, like in Germany's Bavaria, 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, the old buildings outside of Russia usually do not have the typical construction of the Russian onion design. The origin of the design is thought to be the native architectural style of early Rus' tribes. Other types of Eastern Orthodox cupolas include ''helmet domes'' (for example, those of the Assumption Cathedral in Vladimir), Ukrainian ''pear domes'' (Saint Sophia Cathe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 \lam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 to b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodesic Dome
A geodesic dome is a hemispherical thin-shell structure (lattice-shell) based on a geodesic polyhedron. The triangular elements of the dome are structurally rigid and distribute the structural 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 the Carl Zeiss 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 Zeiss plant in Jena, Germany. A larger dome, called "The Wonder of Jena", opened to the public in July 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 rece ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptical Dome
An elliptical dome, or an ''oval dome'', is a dome whose bottom 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 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 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 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 dome is more complex than that of spherical dome, design care is needed. In a geod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a 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 is either an ellipse, or is empty, or is reduced to a single point (this explains the name, meaning "ellipse-like"). It is bounded, which means that it may be enclosed in a sufficiently large sphere. An ellipsoid has three pairwise perpendicular axes of symmetry which intersect at a 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 axes'', or simply axes of the ellipsoid. If the three axes have different lengths, the figure is a triaxial ellipsoid (r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cloister Vault
In architecture, a cloister vault (also called a pavilion vault) is a vault with four concave surfaces (patches of cylinders) meeting at a point above the center of the vault. It can be thought of as formed by two barrel vaults that cross at right angles to each other: the open space within the vault is the intersection of the space within the two barrel vaults, and the solid material that surrounds the vault is the union of the solid material surrounding the two barrel vaults. In this way it differs from a groin vault, which is also formed from two barrel vaults but in the opposite way: in a groin vault, the space is the union of the spaces of two barrel vaults, and the solid material is the intersection. A cloister vault is a square domical vault, a kind of vault with a polygonal cross-section. Domical vaults can have other polygons as cross-sections (especially octagons) rather than being limited to squares. Geometry Any horizontal cross-section of a cloister vault is a squ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
