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Hadwiger
Hugo Hadwiger
Hugo Hadwiger
(23 December 1908 in Karlsruhe, Germany
Karlsruhe, Germany
– 29 October 1981 in Bern, Switzerland)[1] was a Swiss mathematician, known for his work in geometry, combinatorics, and cryptography.Contents1 Biography 2 Mathematical concepts named after Hadwiger 3 Other mathematical contributions 4 Cryptographic work 5 Awards and honors 6 Selected works6.1 Books 6.2 Articles7 ReferencesBiography[edit] Although born in Karlsruhe, Germany, Hadwiger grew up in Bern, Switzerland.[2] He did his undergraduate studies at the University of Bern, where he majored in mathematics but also studied physics and actuarial science.[2] He continued at Bern for his graduate studies, and received his Ph.D
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Karlsruhe, Germany
Karlsruhe (German pronunciation: [ˈkaɐ̯lsˌʁuːə] ( listen); formerly Carlsruhe[citation needed]) is the second-largest city in the state of Baden-Württemberg, in southwest 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
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Euclidean Plane
Two-dimensional space
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, 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
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Special
Special
Special
or specials may refer to:Contents1 Music 2 Film and television 3 Other uses 4 See alsoMusic[edit] Special
Special
(album), a 1992 album by Vesta Williams "Special" (Garbage song), 1998 "Special
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International Standard Book Number
"ISBN" redirects here. For other uses, see ISBN (other).International Standard Book
Book
NumberA 13-digit ISBN, 978-3-16-148410-0, as represented by an EAN-13 bar codeAcronym ISBNIntroduced 1970; 48 years ago (1970)Managing organisation International ISBN AgencyNo. of digits 13 (formerly 10)Check digit Weighted sumExample 978-3-16-148410-0Website www.isbn-international.orgThe International Standard Book
Book
Number (ISBN) is a unique[a][b] numeric commercial book identifier. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.[1] An ISBN is assigned to each edition and variation (except reprintings) of a book. For example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, and 10 digits long if assigned before 2007
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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, Switzerland, was a German publishing house founded in 1961
1961
and closed in 2013.Contents1 Overview 2 Selected publications 3 See also 4 Notes 5 References 6 External linksOverview[edit] The Verlag Harri Deutsch with headquarters in Frankfurt am Main, Germany, was a German publishing house founded in 1961[nb 1] as a spin-off of the scientific bookstore Fachbuchhandlung Harri Deutsch (FHD), which had existed for about a decade earlier.[1] Both were situated near Goethe-Universität Frankfurt am Main. Between 1963[nb 2] and about 1979 the publisher also had an office in Zürich
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Victor Klee
Victor L. Klee, Jr. (September 18, 1925, San Francisco
San Francisco
– August 17, 2007, 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. Born in San Francisco, Vic Klee earned his B.A. degree in 1945 with high honors from 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. After teaching for several years at the University of Virginia, he moved in 1953 to the University of Washington in Seattle, Washington, where he was a faculty member for 54 years.[1] Klee wrote more than 240 research papers
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American Mathematical Monthly
The American Mathematical Monthly
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
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
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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
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Enigma Cipher Machine
The Enigma machines were a series of electro-mechanical rotor cipher machines developed and used in the early- to mid-20th century to protect commercial, diplomatic and military communication. Enigma was invented by the German engineer Arthur Scherbius at the end of World War I.[1] Early models were used commercially from the early 1920s, and adopted by military and government services of several countries, most notably Nazi Germany before and during World War II.[2] Several different Enigma models were produced, but the German military models, having a plugboard, were the most complex. Japanese and Italian models were also in use. Around December 1932, Marian Rejewski, a Polish mathematician and cryptanalyst, while working at the Polish Cipher Bureau, used the theory of permutations and flaws in the German military message encipherment procedures to break the message keys of the plugboard Enigma machine
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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, whose messages were deciphered by the Allies during World War II, producing intelligence code-named 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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Mathematical Morphology
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
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Cross Polytope
In geometry, a cross-polytope,[1] orthoplex,[2] 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 can be chosen as the unit vectors pointing along each co-ordinate axis - i.e. 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
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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.[1] Though abstract, this definition of "projection" formalizes and generalizes the idea of graphical projection
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Bern, Switzerland
The city of Bern
Bern
(German: [bɛrn] ( listen)) or Berne (French: [bɛʁn]; Italian: Berna [ˈbɛrna]; Romansh: Berna  [ˈbɛrnɐ]; Bernese German: Bärn [b̥æːrn]) is the de facto capital of Switzerland, referred to by the Swiss as their (e.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 )
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