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Nine-point Conic
In geometry, the nine-point conic of a complete quadrangle is a conic that passes through the three diagonal points and the six midpoints of sides of the complete quadrangle. The nine-point conic was described by Maxime Bôcher in 1892. The better-known nine-point circle is an instance of Bôcher's conic. The nine-point hyperbola is another instance. Bôcher used the four points of the complete quadrangle as three vertices of a triangle with one independent point: :Given a triangle and a point in its plane, a conic can be drawn through the following nine points: :: the midpoints of the sides of , :: the midpoints of the lines joining to the vertices, and :: the points where these last named lines cut the sides of the triangle. The conic is an ellipse if lies in the interior of or in one of the regions of the plane separated from the interior by two sides of the triangle, otherwise the conic is a hyperbola. Bôcher notes that when is the orthocenter, one obtains the nine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nine Point Conic
9 is a number, numeral, and glyph. 9 or nine may also refer to: Dates * AD 9, the ninth year of the AD era * 9 BC, the ninth year before the AD era * 9, numerical symbol for the month of September Places * Nine, Portugal, a parish in the town of Vila Nova de Famalicão * Planet Nine, a planet proposed to exist in the outer Solar System * Zheleznogorsk, Krasnoyarsk Krai, Russia, a closed town * The 9, a residential portion of Ameritrust Tower in Cleveland People * Louis Niñé (1922–1983), a New York politician whose surname is usually rendered "Nine" * Nine (rapper) (born 1969), a hip hop musician * Tech N9ne (born 1971), an American rapper Fictional characters * The Nine, epithet for the Nazgûl in J. R. R. Tolkien's Middle-earth legendarium * ⑨, a derogatory name for Cirno, an ice fairy from the dōjin game ''Touhou Project'' Literature * ''The Nine (book)'', a 2007 book by Jeffrey Toobin * ''NiNe. magazine'', a magazine for teenage girls * ''Nine'' (manga), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbola
In mathematics, a hyperbola (; pl. hyperbolas or hyperbolae ; adj. hyperbolic ) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows. The hyperbola is one of the three kinds of conic section, formed by the intersection of a plane and a double cone. (The other conic sections are the parabola and the ellipse. A circle is a special case of an ellipse.) If the plane intersects both halves of the double cone but does not pass through the apex of the cones, then the conic is a hyperbola. Hyperbolas arise in many ways: * as the curve representing the reciprocal function y(x) = 1/x in the Cartesian plane, * as the path followed by the shadow of the tip of a sundial, * as the shape of an open orbit (as distinct from a closed elliptical orbit), such as the orbit of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The Edinburgh Mathematical Society
In academia and librarianship, conference proceedings is a collection of academic papers published in the context of an academic conference or workshop. Conference proceedings typically contain the contributions made by researchers at the conference. They are the written record of the work that is presented to fellow researchers. In many fields, they are published as supplements to academic journals; in some, they are considered the main dissemination route; in others they may be considered grey literature. They are usually distributed in printed or electronic volumes, either before the conference opens or after it has closed. A less common, broader :wikt:proceedings, meaning of proceedings are the acts and happenings of an discipline (academia), academic field, a learned society. For example, the title of the ''Acta Crystallographica'' journals is New Latin for "Proceedings in Crystallography"; the ''Proceedings of the National Academy of Sciences of the United States of America' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Bath
(Virgil, Georgics II) , mottoeng = Learn the culture proper to each after its kind , established = 1886 (Merchant Venturers Technical College) 1960 (Bristol College of Science and Technology) 1966 (Bath University of Technology) 1971 (university status) , type = Public , endowment = £8.1 million (2021) , budget = £289.5 million (2020–21) , chancellor = The Earl of Wessex , vice_chancellor = Ian H. White , academic_staff = 2,180 (2020) - including academic atypical staff , students = () , undergrad = () , postgrad = () , doctoral = , city = Bath, Somerset , country = England , coor = , campus = Suburban , free_label = , free = , website www.bath.ac.uk, logo = University of Bath logo.svg , affiliations = ACUAMBAEQUIS EUAUniversities UK Wallace GroupGW4 Sutton 30 SETsquared The University of Bath is a public research university located in Bath, Somerset, United Kingdom. It received its royal charter in 1966, along with a number of other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor & Francis
Taylor & Francis Group is an international company originating in England that publishes books and academic journals. Its parts include Taylor & Francis, Routledge, F1000 (publisher), F1000 Research or Dovepress. It is a division of Informa, Informa plc, a United Kingdom–based publisher and conference company. Overview The company was founded in 1852 when William Francis (chemist), William Francis joined Richard Taylor (editor), Richard Taylor in his publishing business. Taylor had founded his company in 1798. Their subjects covered agriculture, chemistry, education, engineering, geography, law, mathematics, medicine, and social sciences. Francis's son, Richard Taunton Francis (1883–1930), was sole partner in the firm from 1917 to 1930. In 1965, Taylor & Francis launched Wykeham Publications and began book publishing. T&F acquired Hemisphere Publishing in 1988, and the company was renamed Taylor & Francis Group to reflect the growing number of Imprint (trade name), imp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MathWorld
''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at Urbana–Champaign. History Eric W. Weisstein, the creator of the site, was a physics and astronomy student who got into the habit of writing notes on his mathematical readings. In 1995 he put his notes online and called it "Eric's Treasure Trove of Mathematics." It contained hundreds of pages/articles, covering a wide range of mathematical topics. The site became popular as an extensive single resource on mathematics on the web. Weisstein continuously improved the notes and accepted corrections and comments from online readers. In 1998, he made a contract with CRC Press and the contents of the site were published in print and CD-ROM form, titled "CRC Concise Encyclopedia of Mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HathiTrust
HathiTrust Digital Library is a large-scale collaborative repository of digital content from research libraries including content digitized via Google Books and the Internet Archive digitization initiatives, as well as content digitized locally by libraries. 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. The partnership includes over 60 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. The HathiTrust Shared Print Program is a distributed collective collection whose participating libraries have committed to retaining almost 18 million monograph volumes for 25 years, representing three-quarters of HathiT ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant university and the founding campus of the University of California system. Its fourteen colleges and schools offer over 350 degree programs and enroll some 31,800 undergraduate and 13,200 graduate students. Berkeley ranks among the world's top universities. A founding member of the Association of American Universities, Berkeley hosts many leading research institutes dedicated to science, engineering, and mathematics. The university founded and maintains close relationships with three national laboratories at Berkeley, Livermore and Los Alamos, and has played a prominent role in many scientific advances, from the Manhattan Project and the discovery of 16 chemical elements to breakthroughs in computer science and genomics. Berkeley is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circumcircle
In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic. A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle's center is within the polygon. Every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm. Even if a polygon has a circumscribed circle, it may be different from its minimum bounding circle. For example, for an obtuse triangle, the minimum bounding circle has the longest side ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthocenter
In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). This line containing the opposite side is called the ''extended base'' of the altitude. The intersection of the extended base and the altitude is called the ''foot'' of the altitude. The length of the altitude, often simply called "the altitude", is the distance between the extended base and the vertex. The process of drawing the altitude from the vertex to the foot is known as ''dropping the altitude'' at that vertex. It is a special case of orthogonal projection. Altitudes can be used in the computation of the area of a triangle: one half of the product of an altitude's length and its base's length equals the triangle's area. Thus, the longest altitude is perpendicular to the shortest side of the triangle. The altitudes are also related to the sides of the triangle through the trigonometric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ellipse
In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity e, a number ranging from e = 0 (the limiting case of a circle) to e = 1 (the limiting case of infinite elongation, no longer an ellipse but a parabola). An ellipse has a simple algebraic solution for its area, but only approximations for its perimeter (also known as circumference), for which integration is required to obtain an exact solution. Analytically, the equation of a standard ellipse centered at the origin with width 2a and height 2b is: : \frac+\frac = 1 . Assuming a \ge b, the foci are (\pm c, 0) for c = \sqrt. The standard parametric equation is: : (x,y) = (a\cos(t),b\sin(t)) \quad \text \quad 0\leq t\leq 2\pi. Ellipses ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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