|
Orchard-planting Problem
In discrete geometry, the original orchard-planting problem asks for the maximum number of 3-point lines attainable by a configuration of a specific number of points in the plane. It is also called the tree-planting problem or simply the orchard problem. There are also investigations into how many ''k''-point lines there can be. Hallard T. Croft and Paul Erdős proved ''t''''k'' > ''c'' ''n''2 / ''k''3, where ''n'' is the number of points and ''t''''k'' is the number of ''k''-point lines. Their construction contains some ''m''-point lines, where ''m'' > ''k''. One can also ask the question if these are not allowed. Integer sequence Define ''t''3orchard(''n'') to be the maximum number of 3-point lines attainable with a configuration of ''n'' points. For an arbitrary number of points, ''n'', ''t''3orchard(''n'') was shown to be (1/6)''n''2 − O(n) in 1974. The first few values of ''t''3orchard(''n'') are given in the following table . Upp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orchard-planting Problem
In discrete geometry, the original orchard-planting problem asks for the maximum number of 3-point lines attainable by a configuration of a specific number of points in the plane. It is also called the tree-planting problem or simply the orchard problem. There are also investigations into how many ''k''-point lines there can be. Hallard T. Croft and Paul Erdős proved ''t''''k'' > ''c'' ''n''2 / ''k''3, where ''n'' is the number of points and ''t''''k'' is the number of ''k''-point lines. Their construction contains some ''m''-point lines, where ''m'' > ''k''. One can also ask the question if these are not allowed. Integer sequence Define ''t''3orchard(''n'') to be the maximum number of 3-point lines attainable with a configuration of ''n'' points. For an arbitrary number of points, ''n'', ''t''3orchard(''n'') was shown to be (1/6)''n''2 − O(n) in 1974. The first few values of ''t''3orchard(''n'') are given in the following table . Upp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ben Joseph Green
Ben Joseph Green Fellow of the Royal Society, FRS (born 27 February 1977) is a British mathematician, specialising in combinatorics and number theory. He is the Waynflete Professor of Pure Mathematics at the University of Oxford. Early life and education Ben Green was born on 27 February 1977 in Bristol, England. He studied at local schools in Bristol, Bishop Road Primary School and Fairfield Grammar School, competing in the International Mathematical Olympiad in 1994 and 1995. He entered Trinity College, Cambridge in 1995 and completed his Bachelor of Arts, BA in mathematics in 1998, winning the Senior Wrangler (University of Cambridge), Senior Wrangler title. He stayed on for Part III of the Mathematical Tripos, Part III and earned his doctorate under the supervision of Timothy Gowers, with a thesis entitled ''Topics in arithmetic combinatorics'' (2003). During his PhD he spent a year as a visiting student at Princeton University. He was a research Fellow at Trinity College ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Plane Geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the '' Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier,. Euclid was the first to organize these propositions into a logical system in which each result is '' proved'' from axioms and previously proved theorems. The ''Elements'' begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the ''Elements'' states results of what are now called algebra and number theory, explained in geometrical language. For more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geomet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles, spheres, polygons, and so forth. The subject focuses on the combinatorial properties of these objects, such as how they intersect one another, or how they may be arranged to cover a larger object. Discrete geometry has a large overlap with convex geometry and computational geometry, and is closely related to subjects such as finite geometry, combinatorial optimization, digital geometry, discrete differential geometry, geometric graph theory, toric geometry, and combinatorial topology. History Although polyhedra and tessellations had been studied for many years by people such as Kepler and Cauchy, modern discrete geometry has its origins in the late 19th century. Early topics studie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Fields And Their Applications
Finite is the opposite of infinite. It may refer to: * Finite number (other) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marked for person and/or tense or aspect * "Finite", a song by Sara Groves from the album ''Invisible Empires'' See also * * Nonfinite (other) Nonfinite is the opposite of finite * a nonfinite verb A nonfinite verb is a derivative form of a verb unlike finite verbs. Accordingly, nonfinite verb forms are inflected for neither number nor person, and they cannot perform action as the root ... {{disambiguation fr:Fini it:Finito ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The American Mathematical Society
''Proceedings of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. As a requirement, all articles must be at most 15 printed pages. According to the ''Journal Citation Reports'', the journal has a 2018 impact factor of 0.813. Scope ''Proceedings of the American Mathematical Society'' publishes articles from all areas of pure and applied mathematics, including topology, geometry, analysis, algebra, number theory, combinatorics, logic, probability and statistics. Abstracting and indexing This journal is indexed in the following databases: 2011. American Mathematical Society. * |
Discrete And Computational Geometry
'' Discrete & Computational Geometry'' is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986 by Jacob E. Goodman and Richard M. Pollack, the journal publishes articles on discrete geometry and computational geometry. Abstracting and indexing The journal is indexed in: * ''Mathematical Reviews'' * ''Zentralblatt MATH'' * ''Science Citation Index'' * ''Current Contents''/Engineering, Computing and Technology Notable articles The articles by Gil Kalai with a proof of a subexponential upper bound on the diameter of a polyhedron and by Samuel Ferguson on the Kepler conjecture, both published in Discrete & Computational geometry, earned their author the Fulkerson Prize The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at e .... References External link ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometriae Dedicata
''Geometriae Dedicata'' is a mathematical journal, founded in 1972, concentrating on geometry and its relationship to topology, group theory and the theory of dynamical systems. It was created on the initiative of Hans Freudenthal in Utrecht, the Netherlands.. It is published by Springer Netherlands. The Editors-in-Chief An editor-in-chief (EIC), also known as lead editor or chief editor, is a publication's editorial leader who has final responsibility for its operations and policies. The highest-ranking editor of a publication may also be titled editor, managing ... are John R. Parker and Jean-Marc Schlenker.Journal website References External links Springer site Mathematics journals Springer Science+Business Media academic journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theodore Motzkin
Theodore Samuel Motzkin (26 March 1908 – 15 December 1970) was an Israeli-American mathematician. Biography Motzkin's father Leo Motzkin, a Ukrainian Jew, went to Berlin at the age of thirteen to study mathematics. He pursued university studies in the topic and was accepted as a graduate student by Leopold Kronecker, but left the field to work for the Zionist movement before finishing a dissertation. Motzkin grew up in Berlin and started studying mathematics at an early age as well, entering university when he was only 15. He received his Ph.D. in 1934 from the University of Basel under the supervision of Alexander Ostrowski for a thesis on the subject of linear programming (''Beiträge zur Theorie der linearen Ungleichungen'', "Contributions to the Theory of Linear Inequalities", 1936). In 1935, Motzkin was appointed to the Hebrew University in Jerusalem, contributing to the development of mathematical terminology in Hebrew. In 1936 he was an Invited Speaker at the Internat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gabriel Andrew Dirac
Gabriel Andrew Dirac (13 March 1925 – 20 July 1984) was a Hungarian/British mathematician who mainly worked in graph theory. He served as Erasmus Smith's Professor of Mathematics at Trinity College Dublin 1964-1966. In 1952, he gave a sufficient condition for a graph to contain a Hamiltonian circuit. The previous year, he conjectured that n points in the plane, not all collinear, must span at least \lfloor n/2\rfloor two-point lines, where \lfloor x\rfloor is the largest integer not exceeding x. This conjecture was proven true when n is sufficiently large by Green and Tao in 2012. Education Dirac started his studies at St John's College, Cambridge in 1942, but by 1942 the war saw him serving in the aircraft industry. He received his MA in 1949, and moved to the University of London, getting his Ph.D. "On the Colouring of Graphs: Combinatorial topology of Linear Complexes" there under Richard Rado. Career Dirac's main academic positions were at the King's College London (19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Terence Tao
Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory. Tao was born to ethnic Chinese immigrant parents and raised in Adelaide. Tao won the Fields Medal in 2006 and won the Royal Medal and Breakthrough Prize in Mathematics in 2014. He is also a 2006 MacArthur Fellow. Tao has been the author or co-author of over three hundred research papers. He is widely regarded as one of the greatest living mathematicians and has been referred to as the "Mozart of mathematics". Life and career Family Tao's parents are first-generation immigrants from Hong Kong to Australia.''Wen Wei Po'', Page A4, 24 Au ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypocycloid
In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the radius of the larger circle is increased, the hypocycloid becomes more like the cycloid created by rolling a circle on a line. Properties If the smaller circle has radius , and the larger circle has radius , then the parametric equations for the curve can be given by either: :\begin & x (\theta) = (R - r) \cos \theta + r \cos \left(\frac \theta \right) \\ & y (\theta) = (R - r) \sin \theta - r \sin \left( \frac \theta \right) \end or: :\begin & x (\theta) = r (k - 1) \cos \theta + r \cos \left( (k - 1) \theta \right) \\ & y (\theta) = r (k - 1) \sin \theta - r \sin \left( (k - 1) \theta \right) \end If is an integer, then the curve is closed, and has Cusp (singularity), cusps (i.e., sharp corners, where the curve is not Differentiable function, differentiable). Specially for the curve is a straight line and the circles are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
