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Conjugate Hyperbola
In geometry, a conjugate hyperbola to a given hyperbola shares the same asymptotes but lies in the opposite two sectors of the plane compared to the original hyperbola. A hyperbola and its conjugate may be constructed as conic sections obtained from an intersecting plane that meets tangent double cones sharing the same apex. Each cone has an axis, and the plane section is parallel to the plane formed by the axes. Using analytic geometry, the hyperbolas satisfy the symmetric equations :\frac - \frac = 1, with vertices (''a'',0) and (–''a'',0), and :\frac - \frac = -1 (which can also be written as \frac - \frac = 1), with vertices (0,''b'') and (0,–''b''). In case ''a'' = ''b'' they are rectangular hyperbolas, and a reflection of the plane in an asymptote exchanges the conjugates. Similarly, for a non-zero constant ''c'', the coordinate axes form the asymptotes of the conjugate pair xy = c^2 and xy = -c^2. History Apollonius of Perga introduced the conjugate hyperbola through ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Archive
The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including websites, Application software, software applications, music, audiovisual, and print materials. The Archive also advocates a Information wants to be free, free and open Internet. Its mission is committing to provide "universal access to all knowledge". The Internet Archive allows the public to upload and download digital material to its data cluster, but the bulk of its data is collected automatically by its web crawlers, which work to preserve as much of the public web as possible. Its web archiving, web archive, the Wayback Machine, contains hundreds of billions of web captures. The Archive also oversees numerous Internet Archive#Book collections, book digitization projects, collectively one of the world's largest book digitization efforts. ... [...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. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Monist
''The Monist: An International Quarterly Journal of General Philosophical Inquiry'' is a quarterly peer-reviewed academic journal in the field of philosophy. It was established in October 1890 by American publisher Edward C. Hegeler. History Initially the journal published papers not only by philosophers but also by prominent scientists and mathematicians such as Ernst Mach, David Hilbert, Henri Poincaré, Alfred Binet, Pierre Janet, Cesare Lombroso and Ernst Haeckel. The journal helped to professionalize philosophy as an academic discipline in the United States by publishing philosophers such as Charles Sanders Peirce, Ernst Cassirer, John Dewey, Gottlob Frege, Hans-Georg Gadamer, Sidney Hook, C. I. Lewis, Hilary Putnam, Willard Van Orman Quine, and Bertrand Russell. Russell's ''Philosophy of Logical Atomism'' was originally published in full as a series of articles in the journal in 1918–19. After ceasing publication in 1936, the journal resumed publication in 1962 and ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minkowski Space
In physics, Minkowski space (or Minkowski spacetime) () is the main mathematical description of spacetime in the absence of gravitation. It combines inertial space and time manifolds into a four-dimensional model. The model helps show how a spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Mathematician Hermann Minkowski developed it from the work of Hendrik Lorentz, Henri Poincaré, and others said it "was grown on experimental physical grounds". Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical structure by which special relativity is formalized. While the individual components in Euclidean space and time might differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total interval in spacetime between events.This makes spacetime distance an inva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spacetime Diagram
A spacetime diagram is a graphical illustration of locations in space at various times, especially in the special theory of relativity. Spacetime diagrams can show the geometry underlying phenomena like time dilation and length contraction without mathematical equations. The history of an object's location through time traces out a line or curve on a spacetime diagram, referred to as the object's world line. Each point in a spacetime diagram represents a unique position in space and time and is referred to as an event (relativity), event. The most well-known class of spacetime diagrams are known as Minkowski diagrams, developed by Hermann Minkowski in 1908. Minkowski diagrams are two-dimensional graphs that depict events as happening in a universe consisting of one space dimension and one time dimension. Unlike a regular distance-time graph, the distance is displayed on the horizontal axis and time on the vertical axis. Additionally, the time and space units of measurement are c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Minkowski
Hermann Minkowski (22 June 1864 – 12 January 1909) was a mathematician and professor at the University of Königsberg, the University of Zürich, and the University of Göttingen, described variously as German, Polish, Lithuanian-German, or Russian. He created and developed the geometry of numbers and elements of convex geometry, and used geometrical methods to solve problems in number theory, mathematical physics, and the theory of relativity. Minkowski is perhaps best known for his foundational work describing space and time as a four-dimensional space, now known as " Minkowski spacetime", which facilitated geometric interpretations of Albert Einstein's special theory of relativity (1905). Personal life and family Hermann Minkowski was born in the town of Aleksota, the Suwałki Governorate, the Kingdom of Poland, since 1864 part of the Russian Empire, to Lewin Boruch Minkowski, a merchant who subsidized the building of the choral synagogue in Kovno, and Rachel Taub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Salmon
George Salmon (25 September 1819 – 22 January 1904) was a distinguished and influential Irish mathematician and Anglican theologian. After working in algebraic geometry for two decades, Salmon devoted the last forty years of his life to theology. His entire career was spent at Trinity College Dublin, having served as the 32nd Provost of the university from 1888 to 1904. Personal life Salmon was born in Cork in 1819, to Michael Salmon and Helen Weekes (the daughter of the Reverend Edward Weekes). During his boyhood in Cork, where his father Michael was a linen merchant, he attended Hamblin and Porter's School there before starting at Trinity College Dublin in 1833. In 1837, he won a scholarship and graduated from Trinity in 1839 with first-class honours in mathematics. In 1841, at the age of 21, he attained a paid fellowship and teaching position in mathematics at Trinity. In 1845, he was additionally appointed to a position in theology at the university, after having been ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HathiTrust
HathiTrust Digital Library is a large-scale collaborative repository of digital content from research libraries. Its holdings include content digitized via Google Books and the Internet Archive digitization initiatives, as well as content digitized locally by libraries. Etymology ''Hathi'' (), derived from the Sanskrit , is the Hindi word for 'elephant', an animal famed for its long-term memory. History HathiTrust was founded in October 2008 by the twelve universities of the Committee on Institutional Cooperation and the eleven libraries of the University of California. As of 2024, members include more than 219 research libraries across the United States, Canada, and Europe, and is based on a shared governance structure. Costs are shared by the participating libraries and library consortia. The repository is administered by the University of Michigan. The executive director of HathiTrust is Mike Furlough, who succeeded founding director John Wilkin after Wilkin stepped down ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Macfarlane
Alexander Macfarlane FRSE LLD (21 April 1851 – 28 August 1913) was a Scottish logician, physicist, and mathematician. Life Macfarlane was born in Blairgowrie, Scotland, to Daniel MacFarlane (Shoemaker, Blairgowrie) and Ann Small. He studied at the University of Edinburgh. His doctoral thesis "The disruptive discharge of electricity" reported on experimental results from the laboratory of Peter Guthrie Tait. In 1878 Macfarlane spoke at the Royal Society of Edinburgh on algebraic logic as introduced by George Boole. He was elected a Fellow of the Royal Society of Edinburgh. His proposers were Peter Guthrie Tait, Philip Kelland, Alexander Crum Brown, and John Hutton Balfour. The next year he published ''Principles of the Algebra of Logic'' which interpreted Boolean variable expressions with algebraic manipulation. During his life, Macfarlane played a prominent role in research and education. He taught at the universities of Edinburgh and St Andrews, was physics prof ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
