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Octant (geometry)
An octant in solid geometry is one of the eight divisions of a Euclidean three-dimensional coordinate system defined by the signs of the coordinates. It is analogous to the two-dimensional ''quadrant'' and the one-dimensional ''ray''. The generalization of an octant is called ''orthant'' or ''hyperoctant''. Naming and numbering A convention for naming an octant is to give its list of signs, e.g. (+,−,−) or (−,+,−). Octant (+,+,+) is sometimes referred to as the ''first octant'', although similar ordinal name descriptors are not defined for the other seven octants. The advantages of using the (±,±,±) notation are its unambiguousness, and extensibility for higher dimensions. The following table shows the sign tuples together with likely ways to enumerate them. A binary enumeration with − as 1 can be easily generalized across dimensions. A binary enumeration with + as 1 defines the same order as balanced ternary. The Roman enumeration of the quadrants is in Gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cube With Balanced Ternary Labels
A cube or regular hexahedron is a three-dimensional solid object in geometry, which is bounded by six congruent square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It is a type of parallelepiped, with pairs of parallel opposite faces, and more specifically a rhombohedron, with congruent edges, and a rectangular cuboid, with right angles between pairs of intersecting faces and pairs of intersecting edges. It is an example of many classes of polyhedra: Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron. The dual polyhedron of a cube is the regular octahedron. The cube can be represented in many ways, one of which is the graph known as the cubical graph. It can be constructed by using the Cartesian product of graphs. The cube is the three-dimensional hypercube, a family of polytopes also including the two-dimensional square and four-dimensional tesseract. A cube with unit side length is the canonical unit of volume in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gray Code
The reflected binary code (RBC), also known as reflected binary (RB) or Gray code after Frank Gray (researcher), Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit). For example, the representation of the decimal value "1" in binary would normally be "", and "2" would be "". In Gray code, these values are represented as "" and "". That way, incrementing a value from 1 to 2 requires only one bit to change, instead of two. Gray codes are widely used to prevent spurious output from electromechanical switches and to facilitate error correction in digital communications such as digital terrestrial television and some DOCSIS, cable TV systems. The use of Gray code in these devices helps simplify logic operations and reduce errors in practice. Function Many devices indicate position by closing and opening switches. If that device uses natural binary codes, positions 3 and 4 are next to each other but all thre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Octant
In geometry, an octant of a sphere is a spherical triangle with three right angles and three right sides. It is sometimes called a trirectangular (spherical) triangle. It is one face of a spherical octahedron. For a sphere embedded in three-dimensional Euclidean space, the vectors from the sphere's center to each vertex of an octant are the basis vectors of a Cartesian coordinate system relative to which the sphere is a unit sphere. The spherical octant itself is the intersection of the sphere with one octant of space. Uniquely among spherical triangles, the octant is its own polar triangle. The octant can be parametrized using a rational quartic Bézier triangle. The solid angle subtended by a spherical octant is /2 steradian or one-eight of a spat, the solid angle of a full sphere. See also * Trirectangular tetrahedron In geometry, a trirectangular tetrahedron is a tetrahedron where all three face angles at one vertex are right angles. That vertex is calle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octree
An octree is a tree data structure in which each internal node has exactly eight child node, children. Octrees are most often used to partition a three-dimensional space by recursive subdivision, recursively subdividing it into eight Octant (geometry), octants. Octrees are the three-dimensional analog of quadtrees. The word is derived from ''oct'' (Greek root meaning "eight") + ''tree''. Octrees are often used in 3D graphics and 3D game engines. For spatial representation Each node in an octree subdivides the space it represents into eight octant (solid geometry), octants. In a point region (PR) octree (analogous to a point quadtree), the node stores an explicit Point (geometry), three-dimensional point, which is the "center" of the subdivision for that node; the point defines one of the corners for each of the eight children. In a matrix-based (MX) octree (analogous to a region quadtree), the subdivision point is implicitly the center of the space the node represents. The root n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octant (plane Geometry)
A circular sector, also known as circle sector or disk sector or simply a sector (symbol: ⌔), is the portion of a disk (a closed region bounded by a circle) enclosed by two radii and an arc, with the smaller area being known as the ''minor sector'' and the larger being the ''major sector''. In the diagram, is the central angle, the radius of the circle, and is the arc length of the minor sector. The angle formed by connecting the endpoints of the arc to any point on the circumference that is not in the sector is equal to half the central angle. Types A sector with the central angle of 180° is called a '' half-disk'' and is bounded by a diameter and a semicircle. Sectors with other central angles are sometimes given special names, such as quadrants (90°), sextants (60°), and octants (45°), which come from the sector being one quarter, sixth or eighth part of a full circle, respectively. Area The total area of a circle is . The area of the sector can be obtained ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthant
In geometry, an orthant or hyperoctant is the analogue in ''n''-dimensional Euclidean space of a quadrant in the plane or an octant in three dimensions. In general an orthant in ''n''-dimensions can be considered the intersection of ''n'' mutually orthogonal half-spaces. By independent selections of half-space signs, there are 2''n'' orthants in ''n''-dimensional space. More specifically, a closed orthant in R''n'' is a subset defined by constraining each Cartesian coordinate to be nonnegative or nonpositive. Such a subset is defined by a system of inequalities: :ε1''x''1 ≥ 0 ε2''x''2 ≥ 0 · · · ε''n''''x''''n'' ≥ 0, where each ε''i'' is +1 or −1. Similarly, an open orthant in R''n'' is a subset defined by a system of strict inequalities :ε1''x''1 > 0 ε2''x''2 > 0 · ·& ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right-hand Rule
In mathematics and physics, the right-hand rule is a Convention (norm), convention and a mnemonic, utilized to define the orientation (vector space), orientation of Cartesian coordinate system, axes in three-dimensional space and to determine the direction of the cross product of two Euclidean vector, vectors, as well as to establish the direction of the force on a Electric current, current-carrying conductor in a magnetic field. The various right- and left-hand rules arise from the fact that the three axes of three-dimensional space have two possible orientations. This can be seen by holding your hands together with palms up and fingers curled. If the curl of the fingers represents a movement from the first or x-axis to the second or y-axis, then the third or z-axis can point along either right thumb or left thumb. History The right-hand rule dates back to the 19th century when it was implemented as a way for identifying the positive direction of coordinate axes in three dime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Endianness
file:Gullivers_travels.jpg, ''Gulliver's Travels'' by Jonathan Swift, the novel from which the term was coined In computing, endianness is the order in which bytes within a word (data type), word of digital data are transmitted over a data communication medium or Memory_address, addressed (by rising addresses) in computer memory, counting only byte Bit_numbering#Bit significance and indexing, significance compared to earliness. Endianness is primarily expressed as big-endian (BE) or little-endian (LE), terms introduced by Danny Cohen (computer scientist), Danny Cohen into computer science for data ordering in an Internet Experiment Note published in 1980. Also published at The adjective ''endian'' has its origin in the writings of 18th century Anglo-Irish writer Jonathan Swift. In the 1726 novel ''Gulliver's Travels'', he portrays the conflict between sects of Lilliputians divided into those breaking the shell of a boiled egg from the big end or from the little end. By analogy, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roman Numerals
Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, each with a fixed integer value. The modern style uses only these seven: The use of Roman numerals continued long after the Fall of the Western Roman Empire, decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced by Arabic numerals; however, this process was gradual, and the use of Roman numerals persisted in various places, including on clock face, clock faces. For instance, on the clock of Big Ben (designed in 1852), the hours from 1 to 12 are written as: The notations and can be read as "one less than five" (4) and "one less than ten" (9), although there is a tradition favouring the representation of "4" as "" on Roman numeral clocks. Other common uses include year numbers on monuments and buildin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solid Geometry
Solid geometry or stereometry is the geometry of Three-dimensional space, three-dimensional Euclidean space (3D space). A solid figure is the region (mathematics), region of 3D space bounded by a two-dimensional closed surface; for example, a solid ball (mathematics), ball consists of a sphere and its Interior (topology), interior. Solid geometry deals with the measurements of volumes of various solids, including Pyramid (geometry), pyramids, Prism (geometry), prisms (and other polyhedrons), cubes, Cylinder (geometry), cylinders, cone (geometry), cones (and Frustum, truncated cones). History The Pythagoreanism, Pythagoreans dealt with the regular solids, but the pyramid, prism, cone and cylinder were not studied until the Platonism, Platonists. Eudoxus of Cnidus, Eudoxus established their measurement, proving the pyramid and cone to have one-third the volume of a prism and cylinder on the same base and of the same height. He was probably also the discoverer of a proof that t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Balanced Ternary
Balanced ternary is a ternary numeral system (i.e. base 3 with three Numerical digit, digits) that uses a balanced signed-digit representation of the integers in which the digits have the values −1, 0, and 1. This stands in contrast to the standard (unbalanced) ternary system, in which digits have values 0, 1 and 2. The balanced ternary system can represent all integers without using a separate minus sign; the value of the leading non-zero digit of a number has the sign of the number itself. The balanced ternary system is an example of a Non-standard positional numeral systems, non-standard positional numeral system. It was used in some early computers and has also been used to solve balance puzzles. Different sources use different glyphs to represent the three digits in balanced ternary. In this article, T (which resembles a typographical ligature, ligature of the minus sign and 1) represents −1, while 0 and 1 represent themselves. Other conventions include using '−' and '+ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthant
In geometry, an orthant or hyperoctant is the analogue in ''n''-dimensional Euclidean space of a quadrant in the plane or an octant in three dimensions. In general an orthant in ''n''-dimensions can be considered the intersection of ''n'' mutually orthogonal half-spaces. By independent selections of half-space signs, there are 2''n'' orthants in ''n''-dimensional space. More specifically, a closed orthant in R''n'' is a subset defined by constraining each Cartesian coordinate to be nonnegative or nonpositive. Such a subset is defined by a system of inequalities: :ε1''x''1 ≥ 0 ε2''x''2 ≥ 0 · · · ε''n''''x''''n'' ≥ 0, where each ε''i'' is +1 or −1. Similarly, an open orthant in R''n'' is a subset defined by a system of strict inequalities :ε1''x''1 > 0 ε2''x''2 > 0 · ·& ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
