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Gerhard Thomsen
Gerhard Thomsen (23 June 1899 – 4 January 1934) was a German mathematician, probably best known for his work in various branches of geometry. Life Thomsen was born on 23 June 1899 in Hamburg. His father, Georg Thomsen, was a physician. Thomsen grew up in Hamburg and attended the Johanneum ( gymnasium/highschool) from 1908 to 1917. After completing school he served in the army during the last year of World War I. In 1919 he became of the first students at the newly founded University of Hamburg majoring in mathematics and natural science. Aside from a temporary interlude Thomsen studied in Hamburg until 1923. He received a certification to teach at highschools the fall of 1922 and finally his PhD in the summer of the following year. After he worked shortly as an assistant at the Karlsruhe Institute of Technology before returning to Hamburg in a similar capacity in the spring of 1925. While working on his habilitation thesis Thomsen spend one year in Rome on Rockefeller grant to st ... [...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 geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gestapo
The (), abbreviated Gestapo (; ), was the official secret police of Nazi Germany and in German-occupied Europe. The force was created by Hermann Göring in 1933 by combining the various political police agencies of Prussia into one organisation. On 20 April 1934, oversight of the Gestapo passed to the head of the ''Schutzstaffel'' (SS), Heinrich Himmler, who was also appointed Chief of German Police by Hitler in 1936. Instead of being exclusively a Prussian state agency, the Gestapo became a national one as a sub-office of the (SiPo; Security Police). From 27 September 1939, it was administered by the Reich Security Main Office (RSHA). It became known as (Dept) 4 of the RSHA and was considered a sister organisation to the (SD; Security Service). During World War II, the Gestapo played a key role in the Holocaust. After the war ended, the Gestapo was declared a criminal organisation by the International Military Tribunal (IMT) at the Nuremberg trials. History After Adol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1934 Suicides
Events January–February * January 1 – The International Telecommunication Union, a specialist agency of the League of Nations, is established. * January 15 – The 8.0 1934 Nepal–Bihar earthquake, Nepal–Bihar earthquake strikes Nepal and Bihar with a maximum Mercalli intensity scale, Mercalli intensity of XI (''Extreme''), killing an estimated 6,000–10,700 people. * January 26 – A 10-year German–Polish declaration of non-aggression is signed by Nazi Germany and the Second Polish Republic. * January 30 ** In Nazi Germany, the political power of federal states such as Prussia is substantially abolished, by the "Law on the Reconstruction of the Reich" (''Gesetz über den Neuaufbau des Reiches''). ** Franklin D. Roosevelt, President of the United States, signs the Gold Reserve Act: all gold held in the Federal Reserve is to be surrendered to the United States Department of the Treasury; immediately following, the President raises the statutory gold price from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysts
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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometers
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, 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 ''Euclid's Elements, Stoicheia – Elements'' (geometry textbook) * Mozi (c. 468 BC – c. 391 BC) * Plato (427–347 BC) * Theaetetus (mathematician), Theaetetus (c. 417 BC – 369 BC) * Autolycus of Pitane (360–c. 290 BC) – astronomy, spherical geometry * Euclid (fl. 300 BC) – ''Euclid's Elements, Elements'', Euclidean geometry (sometimes called the "father of geometry") * Apolloni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1934 Deaths
Events January–February * January 1 – The International Telecommunication Union, a specialist agency of the League of Nations, is established. * January 15 – The 8.0 1934 Nepal–Bihar earthquake, Nepal–Bihar earthquake strikes Nepal and Bihar with a maximum Mercalli intensity scale, Mercalli intensity of XI (''Extreme''), killing an estimated 6,000–10,700 people. * January 26 – A 10-year German–Polish declaration of non-aggression is signed by Nazi Germany and the Second Polish Republic. * January 30 ** In Nazi Germany, the political power of federal states such as Prussia is substantially abolished, by the "Law on the Reconstruction of the Reich" (''Gesetz über den Neuaufbau des Reiches''). ** Franklin D. Roosevelt, President of the United States, signs the Gold Reserve Act: all gold held in the Federal Reserve is to be surrendered to the United States Department of the Treasury; immediately following, the President raises the statutory gold price from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1899 Births
Events January 1899 * January 1 ** Spanish rule ends in Cuba, concluding 400 years of the Spanish Empire in the Americas. ** Queens and Staten Island become administratively part of New York City. * January 2 – **Bolivia sets up a customs office in Puerto Alonso, leading to the Brazilian settlers there to declare the Republic of Acre in a revolt against Bolivian authorities. **The first part of the Jakarta Kota–Anyer Kidul railway on the island of Java is opened between Batavia Zuid ( Jakarta Kota) and Tangerang. * January 3 – Hungarian Prime Minister Dezső Bánffy fights an inconclusive duel with his bitter enemy in parliament, Horánszky Nándor. * January 4 – **U.S. President William McKinley's declaration of December 21, 1898, proclaiming a policy of benevolent assimilation of the Philippines as a United States territory, is announced in Manila by the U.S. commander, General Elwell Otis, and angers independence activists who had fought against ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomsen's Theorem
Thomsen's theorem, named after Gerhard Thomsen, is a theorem in elementary geometry. It shows that a certain path constructed by line segments being parallel to the edges of a triangle always ends up at its starting point. Consider an arbitrary triangle ''ABC'' with a point ''P''1 on its edge ''BC''. A sequence of points and parallel lines is constructed as follows. The parallel line to ''AC'' through ''P''1 intersects ''AB'' in ''P''2 and the parallel line to BC through ''P''2 intersects AC in ''P''3. Continuing in this fashion the parallel line to AB through ''P''3 intersects BC in ''P''4 and the parallel line to ''AC'' through ''P''4 intersects ''AB'' in ''P''5. Finally the parallel line to ''BC'' through ''P''5 intersects AC in ''P''6 and the parallel line to ''AB'' through ''P''6 intersects ''BC'' in ''P''7. Thomsen's theorem now states that ''P''7 is identical to ''P''1 and hence the construction always leads to a closed path ''P''1''P''2''P''3''P''4''P''5''P''6''P''1 Ref ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying structu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erlangen Program
In mathematics, the Erlangen program is a method of characterizing geometries based on group theory and projective geometry. It was published by Felix Klein in 1872 as ''Vergleichende Betrachtungen über neuere geometrische Forschungen.'' It is named after the University Erlangen-Nürnberg, where Klein worked. By 1872, non-Euclidean geometries had emerged, but without a way to determine their hierarchy and relationships. Klein's method was fundamentally innovative in three ways: :* Projective geometry was emphasized as the unifying frame for all other geometries considered by him. In particular, Euclidean geometry was more restrictive than affine geometry, which in turn is more restrictive than projective geometry. :* Klein proposed that group theory, a branch of mathematics that uses algebraic methods to abstract the idea of symmetry, was the most useful way of organizing geometrical knowledge; at the time it had already been introduced into the theory of equations in the form o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Felix Klein
Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory. His 1872 Erlangen program, classifying geometries by their basic symmetry groups, was an influential synthesis of much of the mathematics of the time. Life Felix Klein was born on 25 April 1849 in Düsseldorf, to Prussian parents. His father, Caspar Klein (1809–1889), was a Prussian government official's secretary stationed in the Rhine Province. His mother was Sophie Elise Klein (1819–1890, née Kayser). He attended the Gymnasium in Düsseldorf, then studied mathematics and physics at the University of Bonn, 1865–1866, intending to become a physicist. At that time, Julius Plücker had Bonn's professorship of mathematics and experimental physics, but by the time Klein became his assistant, in 1866, Plücker's interest wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
