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Roberts's Triangle Theorem
Roberts's triangle theorem, a result in discrete geometry, states that every simple arrangement of lines, arrangement of n lines has at least n-2 triangular faces. Thus, three lines form a triangle, four lines form at least two triangles, five lines form at least three triangles, etc. It is named after Samuel Roberts (mathematician), Samuel Roberts, a British mathematician who published it in 1889. Statement and example The theorem states that every simple arrangement of lines, arrangement of n lines in the Euclidean plane has at least n-2 triangular faces. Here, an arrangement is simple when it has no two parallel lines and no three lines through the same point. A face is one of the polygons formed by the arrangement, but not crossed by any of its lines. Faces may be bounded or infinite, but only the bounded faces with exactly three sides count as triangles for the purposes of the theorem. One way to form an arrangement of n lines with exactly n-2 triangular faces is to choose ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roberts Triangle Theorem N=7
Roberts may refer to: People * Roberts (given name), a Latvian masculine given name * Roberts (surname), a popular surname, especially among the Welsh Places * Roberts (crater), a lunar impact crater on the far side of the Moon ;United States * Roberts, Idaho * Roberts, Illinois * Roberts, Indiana * Roberts, West Virginia * Roberts, Wisconsin * Roberts County, South Dakota * Roberts County, Texas * Mount Roberts (New Hampshire), a summit in the Ossipee Mountains Facilities and structures * The old name of Brandeis/Roberts (MBTA station) * Roberts Stadium (other) Other uses * Roberts class monitor, a class of British warship * USS ''Samuel B. Roberts'' (FFG-58), a U.S. Navy frigate * Roberts Cycles, a cycle manufacturer (also known as Chas. Roberts) * Roberts Radio, a radio manufacturer * .257 Roberts, a medium-powered .25 caliber cartridge * Roberts (company), a Swedish soft drinks manufacturer See also * * * Strebor, a lock manufacturer (Roberts s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperplane
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ''ambient space''. For example, if a space is 3-dimensional then its hyperplanes are the 2-dimensional planes, while if the space is 2-dimensional, its hyperplanes are the 1-dimensional lines. This notion can be used in any general space in which the concept of the dimension of a subspace is defined. In different settings, hyperplanes may have different properties. For instance, a hyperplane of an -dimensional affine space is a flat subset with dimension and it separates the space into two half spaces. While a hyperplane of an -dimensional projective space does not have this property. The difference in dimension between a subspace and its ambient space is known as the codimension of with respect to . Therefore, a necessary and sufficient condition for to be a hyperplane in is for to have codimension one in . Technical description In geometry, a hyperplane of an ''n''-dimensi ... [...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] |
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†... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geombinatorics
Alexander Soifer is a Russian-born American mathematician and mathematics author. His works include over 400 articles and 13 books. Soifer obtained his Ph.D. in 1973 and has been a professor of mathematics at the University of Colorado since 1979. He was visiting fellow at Princeton University from 2002 to 2004, and again in 2006–2007. Soifer also teaches courses on art history and European cinema. His publications include 13 books and over 400 articles. Every spring, Soifer, along with other mathematician colleagues, sponsors the Colorado Mathematical Olympiad (CMO) at the University of Colorado Colorado Springs. Soifer compiles and writes most of the problems for the contest. The CMO was founded by Soifer on April 18, 1983. For the Olympiad's 30th anniversary, the university produced a film about it. In May 2018, in recognition of 35 years of leadership, the judges and winners decided in 2018 to rename the Colorado Mathematical Olympiad to the Soifer Mathematical Olympiad. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete & 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] |
The American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Plane
In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines (namely, parallel lines) that do not intersect. A projective plane can be thought of as an ordinary plane equipped with additional "points at infinity" where parallel lines intersect. Thus ''any'' two distinct lines in a projective plane intersect at exactly one point. Renaissance artists, in developing the techniques of drawing in perspective, laid the groundwork for this mathematical topic. The archetypical example is the real projective plane, also known as the extended Euclidean plane. This example, in slightly different guises, is important in algebraic geometry, topology and projective geometry where it may be denoted variously by , RP2, or P2(R), among other notations. There are many other projective planes, both infinite, such as the complex projective plane, ... [...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] |
Kobon Triangle Problem
The Kobon triangle problem is an unsolved problem in combinatorial geometry first stated by Kobon Fujimura (1903-1983). The problem asks for the largest number ''N''(''k'') of nonoverlapping triangles whose sides lie on an arrangement of ''k'' lines. Variations of the problem consider the projective plane rather than the Euclidean plane, and require that the triangles not be crossed by any other lines of the arrangement.. Known upper bounds Saburo Tamura proved that the number of nonoverlapping triangles realizable by k lines is at most \lfloor k(k-2)/3\rfloor. G. Clément and J. Bader proved more strongly that this bound cannot be achieved when k is congruent to 0 or 2 (mod 6). The maximum number of triangles is therefore at most one less in these cases. The same bounds can be equivalently stated, without use of the floor function In mathematics and computer science, the floor function is the function that takes as input a real number , and gives as output the greatest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
