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Ludwig Danzer
Ludwig Danzer (15 November 1927 – 3 December 2011) was a German geometer working in discrete geometry. He was a student of Hanfried Lenz, starting his career in 1960 with a thesis about "Lagerungsprobleme". Danzer's name is popularized in the concepts of a Danzer set, a set of points that touches all large convex sets, and the Danzer cube, an example of a non-shellable triangulation of the cube. It is an example of a power complex, studied by Danzer in the 1980s. The Danzer cube is example 8.9 in the book "Lectures on Polytopes" by G.M. Ziegler. Danzer also found many new tilings. Ludwig Danzer worked at the Technical University of Dortmund and died on December 3, 2011 after a long illness. Danzer had at least ten students, the most prominent one being Egon Schulte Egon Schulte (born January 7, 1955 in Heggen ( Kreis Olpe), Germany) is a mathematician and a professor of Mathematics at Northeastern University in Boston. He received his Ph.D. in 1980 from the Technical Un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Technical University Of Dortmund
TU Dortmund University (german: Technische Universität Dortmund) is a technical university in Dortmund, North Rhine-Westphalia, Germany with over 35,000 students, and over 6,000 staff including 300 professors, offering around 80 Bachelor's and master's degree programs. It is situated in the Ruhr area, the fourth largest urban area in Europe. The university is highly ranked in terms of its research performance in the areas of physics, electrical engineering, chemistry and economics. The university pioneered the Internet in Germany, and contributed to machine learning (in particular, to support-vector machines, and RapidMiner). History The University of Dortmund (German: ''Universität Dortmund'') was founded in 1968, during the decline of the coal and steel industry in the Ruhr region. Its establishment was seen as an important move in the economic change (''Strukturwandel'') from heavy industry to technology. The university's main areas of research are the natural sciences ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Technical University Of Munich
The Technical University of Munich (TUM or TU Munich; german: Technische Universität München) is a public research university in Munich, Germany. It specializes in engineering, technology, medicine, and applied and natural sciences. Established in 1868 by King Ludwig II of Bavaria, the university now has additional campuses in Garching, Freising, Heilbronn, Straubing, and Singapore, with the Garching campus being its largest. The university is organized into eight schools and departments, and is supported by numerous research centers. It is one of the largest universities in Germany, with 50,000 students and an annual budget of €1,770.3 million (including university hospital). A ''University of Excellence'' under the German Universities Excellence Initiative, TUM is considered the top university in Germany according to major rankings as of 2022 and is among the leading universities in the European Union. Its researchers and alumni include 18 Nobel laureates and 23 Leib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hanfried Lenz
Hanfried Lenz (22 April 1916 in Munich1 June 2013 in Berlin) was a German mathematician, who is mainly known for his work in geometry and combinatorics. Hanfried Lenz was the eldest son of Fritz Lenz an influential German geneticist, who is associated with Eugenics and hence also with the Nazi racial policies during the Third Reich. He was also the older brother of Widukind Lenz, a geneticist. He started to study mathematics and physics at the University of Tübingen, but interrupted his studies from 1935 to 1937 to do his military service. After that he continued to study in Munich, Berlin and Leipzig. In 1939 when World War II broke out in Europe, he became a soldier in the western front and during a vacation he passed the exams for his teacher certification. He married Helene Ranke in 1943 and 1943–45 he worked on radar technology in a laboratory near Berlin. After World War II Hanfried Lenz was classified as a "follower" by the denazification process. He started to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Sauer (mathematician)
Robert Max Friedrich Sauer (16 September 1898 – 22 August 1970) was a German mathematician. He was rector of the Technical University of Munich from 1954 to 1956 and president of the Bavarian Academy of Sciences and Humanities from 1964 to 1970. Early life After graduating from high school in Bamberg and completing his military service in World War I as a non-commissioned officer in the artillery, Sauer studied mathematics and physics at the Technical University of Munich from 1919. In 1925 he received his doctorate. Career After his habilitation in 1926 he taught at the university as lecturer for descriptive geometry. In 1932 he became associate professor and in 1937 full professor of applied mathematics and descriptive geometry at the TH Aachen. During this time, Sauer joined the Nazi Party and became involved in the National Socialist German Lecturers League. Sauer was appointed dean, in part because of his party affiliation. During World War II he worked on ball ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Egon Schulte
Egon Schulte (born January 7, 1955 in Heggen ( Kreis Olpe), Germany) is a mathematician and a professor of Mathematics at Northeastern University in Boston. He received his Ph.D. in 1980 from the Technical University of Dortmund; his doctoral dissertation was on ''Regular Incidence Complexes'' (abstract regular polytope In mathematics, an abstract polytope is an algebraic partially ordered set which captures the dyadic property of a traditional polytope without specifying purely geometric properties such as points and lines. A geometric polytope is said to be ...s). Selected publications * External links * Egon Schulte, Professor, Northeastern University, Department of MathematicsSchulte Publications 1984 - 2010 Living people 1955 births Northeastern University faculty Combinatorialists Technical University of Dortmund alumni People from Olpe (district) {{US-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Danzer Set
In geometry, a Danzer set is a set of points that touches every convex body of unit volume. Ludwig Danzer asked whether it is possible for such a set to have bounded density. Several variations of this problem remain unsolved. Density One way to define the problem more formally is to consider the growth rate of a set S in Euclidean space, defined as the function that maps a real number r to the number of points of S that are within distance r of the origin. Danzer's question is whether it is possible for a Danzer set to have growth expressed in big O notation. If so, this would equal the growth rate of well-spaced point sets like the integer lattice (which is not a Danzer set). It is possible to construct a Danzer set of growth rate that is within a polylogarithmic factor For instance, overlaying rectangular grids whose cells have constant volume but differing aspect ratios can achieve a growth rate Constructions for Danzer sets are known with a somewhat slower growth rate, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometer
A geometer is a mathematician whose area of study is geometry. Some notable geometers and their main fields of work, chronologically listed, are: 1000 BCE to 1 BCE * Baudhayana (fl. c. 800 BC) – Euclidean geometry, geometric algebra * Manava (c. 750 BC–690 BC) – Euclidean geometry * Thales of Miletus (c. 624 BC – c. 546 BC) – Euclidean geometry * Pythagoras (c. 570 BC – c. 495 BC) – Euclidean geometry, Pythagorean theorem * Zeno of Elea (c. 490 BC – c. 430 BC) – Euclidean geometry * Hippocrates of Chios (born c. 470 – 410 BC) – first systematically organized '' Stoicheia – Elements'' (geometry textbook) * Mozi (c. 468 BC – c. 391 BC) * Plato (427–347 BC) * Theaetetus (c. 417 BC – 369 BC) * Autolycus of Pitane (360–c. 290 BC) – astronomy, spherical geometry * Euclid (fl. 300 BC) – '' Elements'', Euclidean geometry (sometimes called the "father of geometry") * Apollonius of Perga (c. 262 BC – c. 190 BC) – Euclidean geometry, conic ... [...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] |
Aperiodic Tiling
An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types (or prototiles) is aperiodic if copies of these tiles can form only non- periodic tilings. The Penrose tilings are the best-known examples of aperiodic tilings. Aperiodic tilings serve as mathematical models for quasicrystals, physical solids that were discovered in 1982 by Dan Shechtman who subsequently won the Nobel prize in 2011. However, the specific local structure of these materials is still poorly understood. Several methods for constructing aperiodic tilings are known. Definition and illustration Consider a periodic tiling by unit squares (it looks like infinite graph paper). Now cut one square into two rectangles. The tiling obtained in this way is non-periodic: there is no non-zero shift that leaves this tiling fixed. But clearly this example is much less interesting than the Penrose tiling. In order t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1927 Births
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album '' Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by Slipk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
