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Petersen–Morley Theorem
In geometry, the Petersen–Morley theorem states that, if , , are three general 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 ... in space, if , , are the lines of shortest distance respectively for the pairs , and , and if , and are the lines of shortest distance respectively for the pairs , and , then there is a single line meeting at right angles all of , , and . The theorem is named after Johannes Hjelmslev (who published his work on this result under his original name Johannes Trolle Petersen) and Frank Morley. References * * * * {{DEFAULTSORT:Petersen-Morley theorem Mathematical theorems Theorems in geometry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...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] |
Johannes Hjelmslev
Johannes Trolle Hjelmslev (; 7 April 1873 – 16 February 1950) was a mathematician from Hørning, Denmark. Hjelmslev worked in geometry and history of geometry. He was the discoverer and eponym of the Hjelmslev transformation, a method for mapping an entire hyperbolic plane into a circle with a finite radius. He was the father of Louis Hjelmslev. Originally named Johannes Trolle Petersen, he changed his patronymic to the surname Hjelmslev to avoid confusion with Julius Petersen. Some of his results are known under his original name, including the Petersen–Morley theorem In geometry, the Petersen–Morley theorem states that, if , , are three general 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), p .... Publications *Johannes Hjelmslev, ''Grundprinciper for den infinitesimale Descriptivgeometri med Anvendelse paa Læren om variable Figurer. Afhandling for d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frank Morley
Frank Morley (September 9, 1860 – October 17, 1937) was a leading mathematician, known mostly for his teaching and research in the fields of algebra and geometry. Among his mathematical accomplishments was the discovery and proof of the celebrated Morley's trisector theorem in elementary plane geometry. He led 50 Ph.D. students, including Clara Latimer Bacon, to their degrees, and was said to be :... one of the more striking figures of the relatively small group of men who initiated that development which, within his own lifetime, brought Mathematics in America from a minor position to its present place in the sun. Life Morley was born in the town of Woodbridge in Suffolk, England. His parents were Elizabeth Muskett and Joseph Roberts Morley, Quakers who ran a china shop. After being educated at Woodbridge School, Morley went on to King's College, Cambridge (B.A., 1884). In 1887, Morley moved to Pennsylvania. He taught at Haverford College until 1900, when he became ch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical Society and the Operational Research Society (ORS). History The Society was established on 16 January 1865, the first president being Augustus De Morgan. The earliest meetings were held in University College, but the Society soon moved into Burlington House, Piccadilly. The initial activities of the Society included talks and publication of a journal. The LMS was used as a model for the establishment of the American Mathematical Society in 1888. Mary Cartwright was the first woman to be President of the LMS (in 1961–62). The Society was granted a royal charter in 1965, a century after its foundation. In 1998 the Society moved from rooms in Burlington House into De Morgan House (named after the society's first president), at 57–5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proceedings Of The Cambridge Philosophical Society
''Mathematical Proceedings of the Cambridge Philosophical Society'' is a mathematical journal published by Cambridge University Press for the Cambridge Philosophical Society. It aims to publish original research papers from a wide range of pure and applied mathematics. The journal, titled ''Proceedings of the Cambridge Philosophical Society'' before 1975, has been published since 1843. Abstracting and indexing The journal is abstracted and indexed in *MathSciNet *Science Citation Index Expanded *Scopus *ZbMATH Open See also *Cambridge Philosophical Society The Cambridge Philosophical Society (CPS) is a scientific society at the University of Cambridge. It was founded in 1819. The name derives from the medieval use of the word philosophy to denote any research undertaken outside the fields of law ... External linksofficial website References Academic journals associated with learned and professional societies Cambridge University Press academic journals Mathematics e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Theorems
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
