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Toroidal Chessboard
Toroidal describes something which resembles or relates to a torus or toroid: Mathematics *Torus *Toroid, a surface of revolution which resembles a torus *Toroidal polyhedron *Toroidal coordinates, a three-dimensional orthogonal coordinate system *Toroidal and poloidal coordinates, directions relative to a torus of reference *Toroidal graph, a graph whose vertices can be placed on a torus such that no edges cross *Toroidal grid network, where an n-dimensional grid network is connected circularly in more than one dimension Engineering *Toroidal inductors and transformers, a type of electrical device *Toroidal and poloidal, directions in magnetohydrodynamics *Toroidal engine, an internal combustion engine with pistons that rotate within a toroidal space *Toroidal CVT, a type of continuously variable transmission *Toroidal reflector, a parabolic reflector which has a different focal distance depending on the angle of the mirror Other uses * Toroidal ring model in theoretical physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus
In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis of revolution passes twice through the circle, the surface is a spindle torus. If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a ''toroid'', as in a square toroid. Real-world objects that approximate a torus of revolution include swim rings, inner tubes and ringette rings. Eyeglass lenses that combine spherical and cylindrical correction are toric lenses. A torus should not be confused with a '' solid torus'', which is formed by r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toroid
In mathematics, a toroid is a surface of revolution with a hole in the middle. The axis of revolution passes through the hole and so does not intersect the surface. For example, when a rectangle is rotated around an axis parallel to one of its edges, then a hollow rectangle-section ring is produced. If the revolved figure is a circle, then the object is called a torus. The term ''toroid'' is also used to describe a toroidal polyhedron. In this context a toroid need not be circular and may have any number of holes. A ''g''-holed ''toroid'' can be seen as approximating the surface of a torus having a topological genus, ''g'', of 1 or greater. The Euler characteristic χ of a ''g'' holed toroid is 2(1-''g'').Stewart, B.; "Adventures Among the Toroids:A Study of Orientable Polyhedra with Regular Faces", 2nd Edition, Stewart (1980). The torus is an example of a toroid, which is the surface of a doughnut. Doughnuts are an example of a solid torus created by rotating a disk, and s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toroidal Polyhedron
In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a -holed torus), having a topological genus () of 1 or greater. Notable examples include the Császár and Szilassi polyhedra. Variations in definition Toroidal polyhedra are defined as collections of polygons that meet at their edges and vertices, forming a manifold as they do. That is, each edge should be shared by exactly two polygons, and at each vertex the edges and faces that meet at the vertex should be linked together in a single cycle of alternating edges and faces, the link of the vertex. For toroidal polyhedra, this manifold is an orientable surface. Some authors restrict the phrase "toroidal polyhedra" to mean more specifically polyhedra topologically equivalent to the (genus 1) torus. In this area, it is important to distinguish embedded toroidal polyhedra, whose faces are flat polygons in three-dimensional Euclidean space that do not cross themselves or each other, from abstract pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toroidal Coordinates
Toroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional bipolar coordinate system about the axis that separates its two foci. Thus, the two foci F_1 and F_2 in bipolar coordinates become a ring of radius a in the xy plane of the toroidal coordinate system; the z-axis is the axis of rotation. The focal ring is also known as the reference circle. Definition The most common definition of toroidal coordinates (\tau, \sigma, \phi) is : x = a \ \frac \cos \phi : y = a \ \frac \sin \phi : z = a \ \frac together with \mathrm(\sigma)=\mathrm(z). The \sigma coordinate of a point P equals the angle F_ P F_ and the \tau coordinate equals the natural logarithm of the ratio of the distances d_ and d_ to opposite sides of the focal ring : \tau = \ln \frac. The coordinate ranges are -\pi<\sigma\le\pi, and Coordinate surfaces Surfaces of con ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toroidal And Poloidal Coordinates
The terms toroidal and poloidal refer to directions relative to a torus of reference. They describe a three-dimensional coordinate system in which the poloidal direction follows a small circular ring around the surface, while the toroidal direction follows a large circular ring around the torus, encircling the central void. The earliest use of these terms cited by the Oxford English Dictionary is by Walter M. Elsasser (1946) in the context of the generation of the Earth's magnetic field by currents in the core, with "toroidal" being parallel to lines of latitude and "poloidal" being in the direction of the magnetic field (i.e. towards the poles). The OED also records the later usage of these terms in the context of toroidally confined plasmas, as encountered in magnetic confinement fusion. In the plasma context, the toroidal direction is the long way around the torus, the corresponding coordinate being denoted by in the slab approximation or or in magnetic coordinates; the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toroidal Graph
In the mathematical field of graph theory, a toroidal graph is a graph that can be embedded on a torus. In other words, the graph's vertices can be placed on a torus such that no edges cross. Examples Any graph that can be embedded in a plane can also be embedded in a torus. A toroidal graph of genus 1 can be embedded in a torus but not in a plane. The Heawood graph, the complete graph K7 (and hence K5 and K6), the Petersen graph (and hence the complete bipartite graph K3,3, since the Petersen graph contains a subdivision of it), one of the Blanuša snarks, and all Möbius ladders are toroidal. More generally, any graph with crossing number 1 is toroidal. Some graphs with greater crossing numbers are also toroidal: the Möbius–Kantor graph, for example, has crossing number 4 and is toroidal. Properties Any toroidal graph has chromatic number at most 7. The complete graph K7 provides an example of a toroidal graph with chromatic number 7. Any triangle-free toroidal graph h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grid Network
Elex Media Komputindo is a publishing company in Indonesia which publishes books, comics, magazines, novels and other print media. Established on January 15, 1985, Elex Media Komputindo is a subsidiary of Kompas Gramedia Group. Elex is headquartered in Tanah Abang, Central Jakarta. Elex Media Komputindo is known as the pioneer of manga publishing in Indonesia, and is now one of the largest comic publishers in Indonesia. History Established in 1985, Elex Media initially published various electronic and computer-themed books. The founder of Kompas, Jakob Oetama, was interested in the potential of manga during his visit to Japan in the late 1980s. In 1991, Elex Media plunged into the manga publishing industry with the publication of Kyoko Mizuki's ''Candy Candy'' manga, originally published by Kodansha. Other manga like '' Kungfu Boy'', ''Doraemon'', and ''Dragon Ball'' began to follow. The decision of the New Order government to allow the establishment of private television sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toroidal Inductors And Transformers
Toroidal inductors and transformers are inductors and transformers which use magnetic cores with a toroidal (ring or donut) shape. They are passivity (engineering), passive electronic components, consisting of a circular ring or donut shaped magnetic core of ferromagnetic material such as laminated core, laminated iron, iron powder, or Ferrite (magnet), ferrite, around which wire is wound. Although closed-core inductors and transformers often used cores with a square shape in the past, the use of toroidal-shaped cores has significantly increased because of their superior electrical performance. The advantage of the toroidal shape is that, due to its symmetry, the amount of magnetic flux that escapes outside the core (leakage flux) is low, therefore it is more efficient and thus radiates less electromagnetic interference (EMI). Toroidal inductors and transformers are used in a wide range of electronic circuits: power supply, power supplies, inverters, and amplifiers, which i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toroidal And Poloidal
Toroidal describes something which resembles or relates to a torus or toroid: Mathematics *Torus *Toroid, a surface of revolution which resembles a torus *Toroidal polyhedron *Toroidal coordinates, a three-dimensional orthogonal coordinate system *Toroidal and poloidal coordinates, directions relative to a torus of reference *Toroidal graph, a graph whose vertices can be placed on a torus such that no edges cross *Toroidal grid network, where an n-dimensional grid network is connected circularly in more than one dimension Engineering *Toroidal inductors and transformers, a type of electrical device *Toroidal and poloidal, directions in magnetohydrodynamics *Toroidal engine, an internal combustion engine with pistons that rotate within a toroidal space *Toroidal CVT, a type of continuously variable transmission *Toroidal reflector, a parabolic reflector which has a different focal distance depending on the angle of the mirror Other uses *Toroidal ring model in theoretical physics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toroidal Engine
A swing-piston engine is a type of internal combustion engine in which the pistons move in a circular motion inside a ring-shaped "cylinder", moving closer and further from each other to provide compression and expansion. Generally two sets of pistons are used, geared to move in a fixed relationship as they rotate around the cylinder. In some versions the pistons oscillate around a fixed center, as opposed to rotating around the entire engine. The design has also been referred to as a oscillating piston engine, vibratory engine when the pistons oscillate instead of rotate, or toroidal engine based on the shape of the "cylinder". Many swing-piston engines have been proposed, but none have been successful. Two attempts in about 2010 are the prototype American-made MYT engine and prototype Russian ORE for use in the Yo-Mobile hybrid car. Both claimed high fuel efficiency and high power-to-weight ratio, but there have been no successful demonstrations of claimed efficiency or that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuously Variable Transmission
A continuously variable transmission (CVT) is an automatic transmission that can change seamlessly through a continuous range of gear ratios. This contrasts with other transmissions that provide a limited number of gear ratios in fixed steps. The flexibility of a CVT with suitable control may allow the engine to operate at a constant RPM while the vehicle moves at varying speeds. CVTs are used in cars, tractors, side-by-sides, motor scooters, snowmobiles, bicycles, and earthmoving equipment. The most common type of CVT uses two pulleys connected by a belt or chain; however, several other designs have also been used at times. Types Pulley-based The most common type of CVT uses a V-belt which runs between two variable-diameter pulleys. The pulleys consist of two cone-shaped halves that move together and apart. The V-belt runs between these two-halves, so the effective diameter of the pulley is dependent on the distance between the two-halves of the pulley. The V-shape ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toroidal Reflector
A toroidal mirror is a reflector whose surface is a section of a torus, defined by two radii of curvature. Such reflectors 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 suffer from astigmatism like a spherical mirror when used in an off-axis geometry, provided the angle of incidence is matched to the design angle. Because they are easier to manufacture, they are much cheaper than ellipsoidal or paraboloidal mirrors for the same surface quality. Toroidal mirrors are used in Yolo telescopes and optical monochromators. In these devices, the source and detectors of the light are not located on the optical axis of the mirror, so the use of a true paraboloid of revolution would cause a distorted image. See also * List of telescope types The following are lists of devices categorized as types of telescopes or devices associated with telescopes. They are broken into major clas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
