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Hyperbolic Orthogonality
In geometry, the relation of hyperbolic orthogonality between two lines separated by the asymptotes of a hyperbola is a concept used in special relativity to define simultaneous events. Two events will be simultaneous when they are on a line hyperbolically orthogonal to a particular time line. This dependence on a certain time line is determined by velocity, and is the basis for the relativity of simultaneity. Geometry Two lines are hyperbolic orthogonal when they are reflections of each other over the asymptote of a given hyperbola. Two particular hyperbolas are frequently used in the plane: The relation of hyperbolic orthogonality actually applies to classes of parallel lines in the plane, where any particular line can represent the class. Thus, for a given hyperbola and asymptote ''A'', a pair of lines (''a'', ''b'') are hyperbolic orthogonal if there is a pair (''c'', ''d'') such that a \rVert c ,\ b \rVert d , and ''c'' is the reflection of ''d'' across ''A''. Similar t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonality And Rotation
In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''. By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in other fields including art and chemistry. Etymology The word comes from the Ancient Greek ('), meaning "upright", and ('), meaning "angle". The Ancient Greek (') and Classical Latin ' originally denoted a rectangle. Later, they came to mean a right triangle. In the 12th century, the post-classical Latin word ''orthogonalis'' came to mean a right angle or something related to a right angle. Mathematics Physics * In optics, polarization states are said to be orthogonal when they propagate independently of each other, as in vertical and horizontal linear polarization or right- and left-handed circular polarization. * In special relativity, a time axis determined by a rapidity of motion is hyperbolic-orthogonal to a space axis of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Involution (mathematics)
In mathematics, an involution, involutory function, or self-inverse function is a function that is its own inverse, : for all in the domain of . Equivalently, applying twice produces the original value. General properties Any involution is a bijection. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x \mapsto -x), reciprocation (x \mapsto 1/x), and complex conjugation (z \mapsto \bar z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concern ...; and reciprocal ciphers such as the ROT13 transformation and the Beaufort cipher, Beaufort polyalphabetic cipher. The Function composition, composition of two invol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gilbert N
Gilbert may refer to: People and fictional characters * Gilbert (given name), including a list of people and fictional characters * Gilbert (surname), including a list of people Places Australia * Gilbert River (Queensland) * Gilbert River (South Australia) Kiribati * Gilbert Islands, a chain of atolls and islands in the Pacific Ocean United States * Gilbert, Arizona, a town * Gilbert, Arkansas, a town * Gilbert, Florida, the airport of Winterhaven * Gilbert, Iowa, a city * Gilbert, Louisiana, a village * Gilbert, Michigan, and unincorporated community * Gilbert, Minnesota, a city * Gilbert, Nevada, ghost town * Gilbert, Ohio, an unincorporated community * Gilbert, Pennsylvania, an unincorporated community * Gilbert, South Carolina, a town * Gilbert, West Virginia, a town * Gilbert, Wisconsin, an unincorporated community * Mount Gilbert (other), various mountains * Gilbert River (Oregon) Outer space * Gilbert (lunar crater) * Gilbert (Martian crater) Ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edwin Bidwell Wilson
Edwin Bidwell Wilson (April 25, 1879 – December 28, 1964) was an American mathematician, statistician, physicist and general polymath. He was the sole protégé of Yale University physicist Josiah Willard Gibbs and was mentor to MIT economist Paul Samuelson. Wilson had a distinguished academic career at Yale and MIT, followed by a long and distinguished period of service as a civilian employee of the US Navy in the Office of Naval Research. In his latter role, he was awarded the Distinguished Civilian Service Award, the highest honorary award available to a civilian employee of the US Navy. Wilson made broad contributions to mathematics, statistics and aeronautics, and is well-known for producing a number of widely used textbooks. He is perhaps best known for his derivation of the eponymously named Wilson score interval, which is a confidence interval used widely in statistics. Life Edwin Bidwell Wilson was born in Hartford, Connecticut to Edwin Horace Wilson (a teacher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rapidity
In relativity, rapidity is commonly used as a measure for relativistic velocity. Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being associated with distance and time coordinates. For one-dimensional motion, rapidities are additive whereas velocities must be combined by Einstein's velocity-addition formula. For low speeds, rapidity and velocity are proportional but, for higher velocities, rapidity takes a larger value, with the rapidity of light being infinite. Using the inverse hyperbolic function , the rapidity corresponding to velocity is where ''c'' is the velocity of light. For low speeds, is approximately . Since in relativity any velocity is constrained to the interval the ratio satisfies . The inverse hyperbolic tangent has the unit interval for its domain and the whole real line for its image; that is, the interval maps onto . History In 1908 Hermann Minkowski ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Relativity
In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference. For example, in the framework of special relativity the Maxwell equations have the same form in all inertial frames of reference. In the framework of general relativity the Maxwell equations or the Einstein field equations have the same form in arbitrary frames of reference. Several principles of relativity have been successfully applied throughout science, whether implicitly (as in Newtonian mechanics) or explicitly (as in Albert Einstein's special relativity and general relativity). Basic concepts Certain principles of relativity have been widely assumed in most scientific disciplines. One of the most widespread is the belief that any law of nature should be the same at all times; and scientific investigations generally assume that laws of nature are the same regardless of the person measuring them. These s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Longmans, Green And Co
Longman, also known as Pearson Longman, is a publishing company founded in London, England, in 1724 and is owned by Pearson PLC. Since 1968, Longman has been used primarily as an imprint by Pearson's Schools business. The Longman brand is also used for the Longman Schools in China and the '' Longman Dictionary''. History Beginnings The Longman company was founded by Thomas Longman (1699 – 18 June 1755), the son of Ezekiel Longman (died 1708), a gentleman of Bristol. Thomas was apprenticed in 1716 to John Osborn, a London bookseller, and at the expiration of his apprenticeship married Osborn's daughter. In August 1724, he purchased the stock and household goods of William Taylor, the first publisher of ''Robinson Crusoe'', for 9s 6d. Taylor's two shops in Paternoster Row, London, were known respectively as the '' Black Swan'' and the ''Ship'', premises at that time having signs rather than numbers, and became the publishing house premises. Longman entered into ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A History Of The Theories Of Aether And Electricity
''A History of the Theories of Aether and Electricity'' is any of three books written by British mathematician Sir Edmund Taylor Whittaker FRS FRSE on the history of electromagnetic theory, covering the development of classical electromagnetism, optics, and aether theories. The book's first edition, subtitled ''from the Age of Descartes to the Close of the Nineteenth Century'', was published in 1910 by Longmans, Green. The book covers the history of aether theories and the development of electromagnetic theory up to the 20th century. A second, extended and revised, edition consisting of two volumes was released in the early 1950s by Thomas Nelson, expanding the book's scope to include the first quarter of the 20th century. The first volume, subtitled ''The Classical Theories'', was published in 1951 and served as a revised and updated edition to the first book. The second volume, subtitled ''The Modern Theories (1900–1926)'', was published two years later in 1953, extende ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space And Time
Space and Time or Time and Space, or ''variation'', may refer to: * '' Space and time'' or ''time and space'' or ''spacetime'', any mathematical model that combines space and time into a single interwoven continuum * Philosophy of space and time Space and time * ''Space and Time'' (magazine), an American magazine featuring speculative fiction * ''Space and Time'' (Doctor Who), 2011 minisode of ''Doctor Who'' * ''Space & Time'' (album), by R.M.C. (Madlib) ** ''Space & Time'' (RMC song), 2010 song off the eponymous album ''Space & Time'' (album) * ''Space & Time'' (EP), by Celldweller ** ''Space & Time'' (Celldweller song), 2012 song off the eponymous EP ''Space & Time'' (EP) * "Space & Time" (song), by Wolf Alice * "Space and Time", a song by The Verve Time and space *'' Time & Space'' (album) 2018 punk album by ''Turnstile'' ** ''Time + Space'' (Turnstile song) 2018 song of the eponymous album '' Time & Space'' See also * * * Spacetime (other) * Timespace (dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World Line
The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept in modern physics, and particularly theoretical physics. The concept of a "world line" is distinguished from concepts such as an "orbit" or a "trajectory" (e.g., a planet's ''orbit in space'' or the ''trajectory'' of a car on a road) by the ''time'' dimension, and typically encompasses a large area of spacetime wherein perceptually straight paths are recalculated to show their ( relatively) more absolute position states—to reveal the nature of special relativity or gravitational interactions. The idea of world lines originates in physics and was pioneered by Hermann Minkowski. The term is now most often used in relativity theories (i.e., special relativity and general relativity). Usage in physics In physics, a world line of an object (approximated as a point in space, e.g., a particle or observer) is the sequence of spacetime events corresp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive differently where and when events occur. Until the 20th century, it was assumed that the three-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time. The physicist Albert Einstein helped develop the idea of spacetime as part of his theory of relativity. Prior to his pioneering work, scientists had two separate theories to explain physical phenomena: Isaac Newton's laws of physics described the motion of massive objects, while James Clerk Maxwell's electromagnetic models explained the properties of light. However, in 1905, Einstein based a work on special relativity on two postulates: * The laws of physics are invari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
