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Hadwiger
HUGO HADWIGER (23 December 1908 in Karlsruhe, Germany
Karlsruhe, Germany
– 29 October 1981 in Bern, Switzerland
Bern, Switzerland
) was a Swiss mathematician , known for his work in geometry , combinatorics , and cryptography . CONTENTS * 1 Biography * 2 Mathematical concepts named after Hadwiger * 3 Other mathematical contributions * 4 Cryptographic work * 5 Awards and honors * 6 Selected works * 6.1 Books * 6.2 Articles * 7 References BIOGRAPHYAlthough born in Karlsruhe, Germany
Karlsruhe, Germany
, Hadwiger grew up in Bern, Switzerland . He did his undergraduate studies at the University of Bern , where he majored in mathematics but also studied physics and actuarial science . He continued at Bern for his graduate studies, and received his Ph.D. in 1936 under the supervision of Willy Scherrer. He was for more than forty years a professor of mathematics at Bern
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Euclidean Plane
TWO-DIMENSIONAL SPACE or BI-DIMENSIONAL SPACE is a geometric setting in which two values (called parameters ) are required to determine the position of an element (i.e., point ). In Mathematics
Mathematics
, it is commonly represented by the symbol ℝ2. For a generalization of the concept, see dimension . Two-dimensional space
Two-dimensional space
can be seen as a projection of the physical universe onto a plane . Usually, it is thought of as a Euclidean space and the two dimensions are called length and width
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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 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 . Since 1997, the journal has been available online at the Mathematical Association of America\'s website. The MAA gives the Lester R
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Asteroid
ASTEROIDS are minor planets , especially those of the inner Solar System . The larger ones have also been called PLANETOIDS. These terms have historically been applied to any astronomical object orbiting the Sun
Sun
that did not show the disc of a planet and was not observed to have the characteristics of an active comet . As minor planets in the outer Solar System
Solar System
were discovered and found to have volatile-based surfaces that resemble those of comets, they were often distinguished from asteroids of the asteroid belt . In this article, the term "asteroid" refers to the minor planets of the inner Solar System including those co-orbital with Jupiter
Jupiter
. There are millions of asteroids, many thought to be the shattered remnants of planetesimals , bodies within the young Sun's solar nebula that never grew large enough to become planets
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Mathematical Morphology
MATHEMATICAL MORPHOLOGY (MM) is a theory and technique for the analysis and processing of geometrical structures, based on set theory , lattice theory , topology , and random functions . MM is most commonly applied to digital images , but it can be employed as well on graphs , surface meshes , solids , and many other spatial structures. Topological and geometrical continuous -space concepts such as size, shape , convexity , connectivity , and geodesic distance , were introduced by MM on both continuous and discrete spaces . MM is also the foundation of morphological image processing , which consists of a set of operators that transform images according to the above characterizations. The basic morphological operators are erosion , dilation , opening and closing . MM was originally developed for binary images , and was later extended to grayscale functions and images. The subsequent generalization to complete lattices is widely accepted today as MM's theoretical foundation
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Rotor Machine
In cryptography , a ROTOR MACHINE is an electro-mechanical stream cipher device used for encrypting and decrypting secret messages. Rotor machines were the cryptographic state-of-the-art for a prominent period of history; they were in widespread use in the 1920s–1970s. The most famous example is the German Enigma machine
Enigma machine
, whose messages were deciphered by the Allies during World War II, producing intelligence code-named Ultra
Ultra
. The primary component is a set of rotors, also termed wheels or drums, which are rotating disks with an array of electrical contacts on either side. The wiring between the contacts implements a fixed substitution of letters, replacing them in some complex fashion
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Hadwiger–Finsler Inequality
INEQUALITY may refer to: In economics: * Economic inequality
Economic inequality
* Income inequality metrics
Income inequality metrics
* International inequality * List of countries by wealth inequality * List of countries by income inequality In healthcare: * Health equity In mathematics: * Inequality (mathematics)
Inequality (mathematics)
* Inequalities (book) (1934), a mathematics book by G. H. Hardy
G. H. Hardy
, J. E. Littlewood , and G
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Pedoe's Inequality
In geometry , PEDOE\'S INEQUALITY (also NEUBERG-PEDOE INEQUALITY), named after Daniel Pedoe (1910-1998) and Joseph Jean Baptiste Neuberg (1840-1926), states that if a, b, and c are the lengths of the sides of a triangle with area ƒ, and A, B, and C are the lengths of the sides of a triangle with area F, then A 2 ( b 2 + c 2 a 2 ) + B 2 ( a 2 + c 2 b 2 ) + C 2 ( a 2 + b 2 c 2 ) 16 F f , {displaystyle A^{2}(b^{2}+c^{2}-a^{2})+B^{2}(a^{2}+c^{2}-b^{2})+C^{2}(a^{2}+b^{2}-c^{2})geq 16Ff,,} with equality if and only if the two triangles are similar with pairs of corresponding sides (A, a), (B, b), and (C, c). The expression on the left is not only symmetric under any of the six permutations of the set { (A, a), (B, b), (C, c) } of pairs, but also—perhaps not so obviously—remains the same if a is interchanged with A and b with B and c with C
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Special
SPECIAL or SPECIALS may refer to: CONTENTS * 1 Music * 2 Film and television * 3 Other uses * 4 See also MUSIC * Special (album) , a 1992 album by Vesta Williams * "Special" (Garbage song) , 1998 * "Special" (Mew song) , 2005 * "Special" (Stephen Lynch song) , 2000 * The Specials
The Specials
, a British band * "Special", a song by Violent Femmes on The Blind Leading the Naked * "Special", a song on
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Orthogonal Projection
In linear algebra and functional analysis , a PROJECTION is a linear transformation P from a vector space to itself such that P 2 = P. That is, whenever P is applied twice to any value, it gives the same result as if it were applied once (idempotent ). It leaves its image unchanged. Though abstract, this definition of "projection" formalizes and generalizes the idea of graphical projection . One can also consider the effect of a projection on a geometrical object by examining the effect of the projection on points in the object
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Verlag Harri Deutsch
The VERLAG HARRI DEUTSCH (VHD, HD) with headquarters in Frankfurt am Main , Germany, as well as in Zürich
Zürich
and Thun
Thun
, Switzerland, was a German publishing house founded in 1961
1961
and closed in 2013. CONTENTS * 1 Overview * 2 Selected publications * 3 See also * 4 Notes * 5 References * 6 External links OVERVIEWThe Verlag Harri Deutsch with headquarters in Frankfurt am Main
Frankfurt am Main
, Germany, was a German publishing house founded in 1961
1961
as a spin-off of the scientific bookstore Fachbuchhandlung Harri Deutsch (FHD), which had existed for about a decade earlier. Both were situated near Goethe-Universität Frankfurt am Main
Frankfurt am Main
. Between 1963 and about 1979 the publisher also had an office in Zürich
Zürich

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Mathematics Genealogy Project
The MATHEMATICS GENEALOGY PROJECT is a web-based database for the academic genealogy of mathematicians . By 24 April 2017, it contained information on 211,735 mathematical scientists who contributed to research-level mathematics. For a typical mathematician, the project entry includes graduation year, thesis title, alma mater , doctoral advisor , and doctoral students. CONTENTS * 1 Origin of the database * 2 Mission * 3 Scope * 4 Accuracy of information and other criticisms * 5 See also * 6 References * 7 External links ORIGIN OF THE DATABASEThe project grew out of founder Harry Coonce 's desire to know the name of his advisor's advisor. Coonce was Professor of Mathematics at Minnesota State University, Mankato , at the time of the project's founding, and the project went online there in fall 1997. Coonce retired from Mankato in 1999, and in fall 2002 the university decided that it would no longer support the project
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Victor Klee
VICTOR L. KLEE, JR. (September 18, 1925, San Francisco
San Francisco
– August 17, 2007, Lakewood, Ohio
Lakewood, Ohio
) was a mathematician specialising in convex sets , functional analysis , analysis of algorithms , optimization , and combinatorics . He spent almost his entire career at the University of Washington in Seattle
Seattle
. Born in San Francisco
San Francisco
, Vic Klee earned his B.A. degree in 1945 with high honors from Pomona College
Pomona College
, majoring in mathematics and chemistry. He did his graduate studies, including a thesis on Convex Sets in Linear Spaces, and received his PhD
PhD
in mathematics from the University of Virginia
University of Virginia
in 1949
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Karlsruhe, Germany
KARLSRUHE (German pronunciation: ( listen ); formerly CARLSRUHE) is the second-largest city in the state of Baden-Württemberg , in southwest Germany
Germany
, near the French-German border. It has a population of 307,755. The city is the seat of the two highest courts in Germany: the Federal Constitutional Court and the Federal Court of Justice . Its most remarkable building is Karlsruhe Palace , which was built in 1715
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Cross Polytope
In geometry , a CROSS-POLYTOPE, ORTHOPLEX, HYPEROCTAHEDRON, or COCUBE is a regular , convex polytope that exists in n-dimensions . A 2-orthoplex is a square, a 3-orthoplex is a regular octahedron , and a 4-orthoplex is a 16-cell . Its facets are simplexes of the previous dimension, while the cross-polytope's vertex figure is another cross-polytope from the previous dimension. The vertices of a cross-polytope are all the permutations of (±1, 0, 0, …, 0). The cross-polytope is the convex hull of its vertices. The n-dimensional cross-polytope can also be defined as the closed unit ball (or, according to some authors, its boundary) in the ℓ1-norm on Rn: { x R n : x 1 1 } . {displaystyle {xin mathbb {R} ^{n}:x_{1}leq 1}.} In 1 dimension the cross-polytope is simply the line segment , in 2 dimensions it is a square (or diamond) with vertices {(±1, 0), (0, ±1)}
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Perimeter
A PERIMETER is a path that surrounds a two-dimensional shape . The term may be used either for the path or its length—it can be thought of as the length of the outline of a shape. The perimeter of a circle or ellipse is called its circumference . Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel (its circumference) describes how far it will roll in one revolution . Similarly, the amount of string wound around a spool is related to the spool's perimeter
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