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Regulus (geometry)
In three-dimensional space, a regulus ''R'' is a set of skew lines, every point of which is on a transversal which intersects an element of ''R'' only once, and such that every point on a transversal lies on a line of ''R''. The set of transversals of ''R'' forms an opposite regulus ''S''. In \mathbb^ the union ''R'' ∪ ''S'' is the ruled surface of a hyperboloid of one sheet. Three skew lines determine a regulus: :The locus of lines meeting three given skew lines is called a ''regulus''. Gallucci's theorem shows that the lines meeting the generators of the regulus (including the original three lines) form another "associated" regulus, such that every generator of either regulus meets every generator of the other. The two reguli are the two systems of generators of a ''ruled quadric''. According to Charlotte Scott, "The regulus supplies extremely simple proofs of the properties of a conic...the theorems of Chasles, Brianchon, and Pascal ..." In a finite geometry PG(3, ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruled Hyperboloid
''Ruled'' is the fifth full-length LP album, LP by The Giraffes (Brooklyn band), The Giraffes. Drums, bass and principal guitar tracks recorded at The Bunker in Brooklyn, NY. Vocals and additional guitars recorded at Strangeweather in Brooklyn, NY. Mixed at Studio G in Brooklyn, NY by Joel Hamilton. Mastered by Julian Silva at On Air Mastering. Produced by The Giraffes and Joel Hamilton. Track listing All songs written by The Giraffes. #"The Border" - 3:10 #"The Bed" - 5:58 #"The City" - 6:47 #"The Kids" - 3:35 #"The Invasion" - 2:23 #"The Store" - 6:32 #"The War of Hormones" - 7:59 #"The Occupation" - 13:24 Personnel * Aaron Lazar - vocals * Damien Paris - guitar * Jens Carstensen - bass * Andrew Totolos - drums * James SK Wān – bamboo flute * Joel Hamilton - engineer, mixer * Marc Alan Goodman - engineer * Titfinger - art direction References External links The Giraffes // Ruled at Crustacean Records {{Authority control 2011 albums The Giraffes (Brookl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Geometry
A finite geometry is any geometry, geometric system that has only a finite set, finite number of point (geometry), points. The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based on the graphics displayed on a computer screen, where the pixels are considered to be the points, would be a finite geometry. While there are many systems that could be called finite geometries, attention is mostly paid to the finite projective space, projective and affine spaces because of their regularity and simplicity. Other significant types of finite geometry are finite Möbius plane, Möbius or inversive planes and Laguerre planes, which are examples of a general type called Benz planes, and their higher-dimensional analogs such as higher finite inversive geometry, inversive geometries. Finite geometries may be constructed via linear algebra, starting from vector spaces over a finite field; the affine and projective planes so const ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spread (projective Geometry)
A frequently studied problem in finite geometry is to identify ways in which an object can be covered by other simpler objects such as points, lines, and planes. In projective geometry, a specific instance of this problem that has numerous applications is determining whether, and how, a projective space can be covered by pairwise disjoint subspaces which have the same dimension; such a partition is called a spread. Specifically, a spread of a projective space PG(d,K), where d \geq 1 is an integer and K a division ring, is a set of r-dimensional subspaces, for some 0 < r < d such that every point of the space lies in exactly one of the elements of the spread. Spreads are particularly well-studied in projective geometries over finite fields, though some notable results apply to infinite projective geometries as well. In the finite case, the foundational work on spreads appears in André and independently in Bruck-Bose in connection with ... [...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] |
Analytic Geometry
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, Aerospace engineering, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including Algebraic geometry, algebraic, Differential geometry, differential, Discrete geometry, discrete and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical definitions and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert J
The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of '' Hruod'' () "fame, glory, honour, praise, renown, godlike" and ''berht'' "bright, light, shining"). It is the second most frequently used given name of ancient Germanic origin.Reaney & Wilson, 1997. ''Dictionary of English Surnames''. Oxford University Press. It is also in use as a surname. Another commonly used form of the name is Rupert. After becoming widely used in Continental Europe, the name entered England in its Old French form ''Robert'', where an Old English cognate form (''Hrēodbēorht'', ''Hrodberht'', ''Hrēodbēorð'', ''Hrœdbœrð'', ''Hrœdberð'', ''Hrōðberχtŕ'') had existed before the Norman Conquest. The feminine version is Roberta. The Italian, Portuguese, and Spanish form is Roberto. Robert is also a common name in many Germanic languages, including En ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The Royal Society
''Proceedings of the Royal Society'' is the main research journal of the Royal Society. The journal began in 1831 and was split into two series in 1905: * Series A: for papers in physical sciences and mathematics. * Series B: for papers in life sciences. Many landmark scientific discoveries are published in the Proceedings, making it one of the most important science journals in history. The journal contains several articles written by prominent scientists such as Paul Dirac, Werner Heisenberg, Ernest Rutherford, Erwin Schrödinger, William Lawrence Bragg, Lord Kelvin, J.J. Thomson, James Clerk Maxwell, Dorothy Hodgkin and Stephen Hawking. In 2004, the Royal Society began '' The Journal of the Royal Society Interface'' for papers at the interface of physical sciences and life sciences. History The journal began in 1831 as a compilation of abstracts of papers in the '' Philosophical Transactions of the Royal Society'', the older Royal Society publication, that began in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Edge (mathematician)
William Leonard Edge FRSE (8 November 1904 – 27 September 1997) was a British mathematician most known for his work in finite geometry. Students knew him as WLE. Life Born in Stockport to schoolteacher parents (his father William Henry Edge being a headmaster), Edge attended Stockport Grammar School before winning a place at Trinity College, Cambridge in 1923 with an entrance scholarship, later graduating MA DSc. In 1928 Trinity College made him a Research Fellow and he was also an Allen Scholar. William Edge was a geometry student of H. F. Baker at Cambridge. Edge's dissertation extended Luigi Cremona’s 1868 delineation of the quadric ruled surfaces in projective 3-space RP3. Edge made a "systematic classification of the quintic and sextic ruled surfaces of three-dimensional projective space." In 1932 E. T. Whittaker invited Edge to lecture at University of Edinburgh. An anachronism, Edge never drove a motor car and disdained the mass-media of radio and television; he was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessment to form Cambridge University Press and Assessment under Queen Elizabeth II's approval in August 2021. With a global sales presence, publishing hubs, and offices in more than 40 countries, it published over 50,000 titles by authors from over 100 countries. Its publications include more than 420 academic journals, monographs, reference works, school and university textbooks, and English language teaching and learning publications. It also published Bibles, runs a bookshop in Cambridge, sells through Amazon, and has a conference venues business in Cambridge at the Pitt Building and the Sir Geoffrey Cass Sports and Social Centre. It also served as the King's Printer. Cambridge University Press, as part of the University of Cambridge, was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albrecht Beutelspacher
Albrecht Beutelspacher (born 5 June 1950) is a German mathematician and founder of the Mathematikum. He is a professor emeritus at the University of Giessen, where he held the chair for geometry and discrete mathematics from 1988 to 2018. Biography Beutelspacher studied from 1969 to 1973 math, physics and philosophy at the University of Tübingen and received his PhD 1976 from the University of Mainz. His PhD advisor was Judita Cofman. From 1982 to 1985 he was an associate professor at the University of Mainz and from 1985 to 1988 he worked at a research department of Siemens. From 1988 to 2018 he was a tenured professor for geometry and discrete mathematics at the University of Giessen University of Giessen, official name Justus Liebig University Giessen (), is a large public research university in Giessen, Hesse, Germany. It is one of the oldest institutions of higher education in the German-speaking world. It is named afte .... He became a well-known popularizer of math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulletin Of The American Mathematical Society
The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. It also publishes, by invitation only, book reviews and short ''Mathematical Perspectives'' articles. History It began as the ''Bulletin of the New York Mathematical Society'' and underwent a name change when the society became national. The Bulletin's function has changed over the years; its original function was to serve as a research journal for its members. Indexing The Bulletin is indexed in Mathematical Reviews, Science Citation Index, ISI Alerting Services, CompuMath Citation Index, and Current Contents/Physical, Chemical & Earth Sciences. See also *'' Journal of the American Mathematical Society'' *'' Memoirs of the American Mathematical Society'' *'' Notices of the American Mathematical Society'' *'' Proceedings of the Ame ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skew Lines
In three-dimensional geometry, skew lines are two Line (geometry), lines that do not Line-line intersection, intersect and are not Parallel (geometry), parallel. A simple example of a pair of skew lines is the pair of lines through opposite edges of a regular tetrahedron. Two lines that both lie in the same plane must either cross each other or be parallel, so skew lines can exist only in three or more dimensions. Two lines are skew if and only if they are not coplanar. General position If four points are chosen at random Uniform distribution (continuous), uniformly within a unit cube, they will almost surely define a pair of skew lines. After the first three points have been chosen, the fourth point will define a non-skew line if, and only if, it is coplanar with the first three points. However, the plane through the first three points forms a subset of measure zero of the cube, and the probability that the fourth point lies on this plane is zero. If it does not, the lines defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
