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Franz Taurinus
Franz Adolph Taurinus (15 November 1794 – 13 February 1874) was a Germans, German mathematician who is known for his work on non-Euclidean geometry. Life Franz Taurinus was the son of Julius Ephraim Taurinus, a court official of the Count of Erbach-Schönberg, and Luise Juliane Schweikart. He studied law in Heidelberg, Gießen and Göttingen. He lived as a private scholar in Cologne. Hyperbolic geometry Taurinus corresponded with his uncle Ferdinand Karl Schweikart (1780-1859), who was a law professor in Königsberg, among other things about mathematics. Schweikart examined a model (after Giovanni Girolamo Saccheri and Johann Heinrich Lambert) in which the parallel postulate is not satisfied, and in which the sum of three angles of a triangle is less than two right angles (which is now called hyperbolic geometry). While Schweikart never published his work (which he called "astral geometry"), he sent a short summary of its main principles by letter to Carl Friedrich Gauß. Mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Germans
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Hyperbolic Law Of Cosines
In hyperbolic geometry, the "law of cosines" is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar law of cosines from plane trigonometry, or the spherical law of cosines in spherical trigonometry. It can also be related to the relativistic velocity addition formula.Barrett, J.F. (2006), The hyperbolic theory of relativity MathpagesVelocity Compositions and Rapidity/ref> History Describing relations of hyperbolic geometry, it was shown by Franz Taurinus (1826) that the spherical law of cosines can be related to spheres of imaginary radius, thus he arrived at the hyperbolic law of cosines in the form: :A=\operatorname\frac which was also shown by Nikolai Lobachevsky (1830): :\cos A\sin b\sin c-\cos b\cos c=\cos a;\quad ,\ b,\ crightarrow\left \sqrt,\ b\sqrt,\ c\sqrt\right Ferdinand Minding (1840) gave it in relation to surfaces of constant negative curvature: :\cos a\sqrt=\cos b\sqrt\cdot\cos c\sqrt+\sin b\sqrt\cdot\sin c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1874 Deaths
Events January–March * January 1 – New York City annexes The Bronx. * January 2 – Ignacio María González becomes head of state of the Dominican Republic for the first time. * January 3 – Third Carlist War – Battle of Caspe: Campaigning on the Ebro in Aragon for the Spanish Republican Government, Colonel Eulogio Despujol surprises a Carlist force under Manuel Marco de Bello at Caspe, northeast of Alcañiz. In a brilliant action the Carlists are routed, losing 200 prisoners and 80 horses, while Despujol is promoted to Brigadier and becomes Conde de Caspe. * January 20 – The Pangkor Treaty (also known as the Pangkor Engagement), by which the British extended their control over first the Sultanate of Perak, and later the other independent Malay States, is signed. * January 23 **Prince Alfred, Duke of Edinburgh, second son of Queen Victoria, marries Grand Duchess Maria Alexandrovna of Russia, only daughter of Tsar Alexander III of Russia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1794 Births
Events January–March * January 1 – The Stibo Group is founded by Niels Lund as a printing company in Aarhus (Denmark). * January 13 – The U.S. Congress enacts a law providing for, effective May 1, 1795, a United States flag of 15 stars and 15 stripes, in recognition of the recent admission of Vermont and Kentucky as the 14th and 15th states. A subsequent act restores the number of stripes to 13, but provides for additional stars upon the admission of each additional state. * January 21 – King George III of Great Britain delivers the speech opening Parliament and recommends a continuation of Britain's war with France. * February 4 – French Revolution: The National Convention of the French First Republic abolishes slavery. * February 8 – Wreck of the Ten Sail on Grand Cayman. * February 11 – The first session of the United States Senate is open to the public. * March 4 – The Eleventh Amendment to the United States Constituti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Regensburg
The University of Regensburg (german: link=no, Universität Regensburg) is a public research university located in the medieval city of Regensburg, Bavaria, a city that is listed as a UNESCO World Heritage Site. The university was founded on 18 July 1962 by the Landtag of Bavaria as the fourth full-fledged university in Bavaria. Following groundbreaking in 1965, the university officially opened to students during the 1967–1968 winter semester, initially housing faculties in Law and Business Sciences and Philosophy. During the summer semester of 1968 the faculty of Theology was created. Currently, the University of Regensburg houses eleven faculties. The university actively participates in the European Union's SOCRATES programme as well as several TEMPUS programmes. Its most famous academic, the previous Pope Benedict XVI, served as a professor there until 1977 and formally retained his chair in theology. History Attempts to establish a university in Regensburg had been advoc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Bonn
The Rhenish Friedrich Wilhelm University of Bonn (german: Rheinische Friedrich-Wilhelms-Universität Bonn) is a public research university located in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the ( en, Rhine University) on 18 October 1818 by Frederick William III, as the linear successor of the ( en, Academy of the Prince-elector of Cologne) which was founded in 1777. The University of Bonn offers many undergraduate and graduate programs in a range of subjects and has 544 professors. The University of Bonn is a member of the U15 (German universities), German U15 association of major research-intensive universities in Germany and has the title of "University of Excellence" under the German Universities Excellence Initiative; it is consistently ranked amongst the best German universities in the world rankings and is one of the most research intensive universities in Germany. Bonn has 6 Clusters of Excellence, the most of any German university; t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Georg Ohm
Georg Simon Ohm (, ; 16 March 1789 – 6 July 1854) was a German physicist and mathematician. As a school teacher, Ohm began his research with the new electrochemical cell, invented by Italian scientist Alessandro Volta. Using equipment of his own creation, Ohm found that there is a direct proportionality between the potential difference (voltage) applied across a conductor and the resultant electric current. This relation is called Ohm's law, and the ohm, the unit of electrical resistance, is named after him. Biography Early life Georg Simon Ohm was born into a Protestant family in Erlangen, Brandenburg-Bayreuth (then part of the Holy Roman Empire), son to locksmith Johann Wolfgang Ohm, and Maria Elizabeth Beck, daughter of a tailor in Erlangen. Although his parents had not been formally educated, Ohm's father was a respected man who had educated himself to a high level and was able to give his sons an excellent education through his own teachings. Of the seven children of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
János Bolyai
János Bolyai (; 15 December 1802 – 27 January 1860) or Johann Bolyai, was a Hungarian mathematician, who developed absolute geometry—a geometry that includes both Euclidean geometry and hyperbolic geometry. The discovery of a consistent alternative geometry that might correspond to the structure of the universe helped to free mathematicians to study abstract concepts irrespective of any possible connection with the physical world. Early life Bolyai was born in the Hungarian town of Kolozsvár, Grand Principality of Transylvania (now Cluj-Napoca in Romania), the son of Zsuzsanna Benkő and the well-known mathematician Farkas Bolyai. By the age of 13, he had mastered calculus and other forms of analytical mechanics, receiving instruction from his father. He studied at the Imperial and Royal Military Academy (TherMilAk) in Vienna from 1818 to 1822. Career Bolyai became so obsessed with Euclid's parallel postulate that his father, who had pursued the same subject for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nikolai Lobachevsky
Nikolai Ivanovich Lobachevsky ( rus, Никола́й Ива́нович Лобаче́вский, p=nʲikɐˈlaj ɪˈvanəvʲɪtɕ ləbɐˈtɕɛfskʲɪj, a=Ru-Nikolai_Ivanovich_Lobachevsky.ogg; – ) was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry, and also for his fundamental study on Dirichlet integrals, known as the Lobachevsky integral formula. William Kingdon Clifford called Lobachevsky the "Copernicus of Geometry" due to the revolutionary character of his work. Biography Nikolai Lobachevsky was born either in or near the city of Nizhny Novgorod in the Russian Empire (now in Nizhny Novgorod Oblast, Russia) in 1792 to parents of Russian and Polish origin – Ivan Maksimovich Lobachevsky and Praskovia Alexandrovna Lobachevskaya.Victor J. Katz. ''A history of mathematics: Introduction''. Addison-Wesley. 2009. p. 842. Stephen Hawking. ''God Created the Integers: The Mathematical Br ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedrich Engel (mathematician)
Friedrich Engel (26 December 1861 – 29 September 1941) was a German mathematician. Engel was born in Lugau, Saxony, as the son of a Lutheran pastor. He attended the Universities of both Leipzig and Berlin, before receiving his doctorate from Leipzig in 1883. Engel studied under Felix Klein at Leipzig, and collaborated with Sophus Lie for much of his life. He worked at Leipzig (1885–1904), Greifswald (1904–1913), and Giessen (1913–1931). He died in Giessen. Engel was the co-author, with Sophus Lie, of the three volume work ''Theorie der Transformationsgruppen'' (publ. 1888–1893; tr., "Theory of transformation groups"). Engel was the editor of the collected works of Sophus Lie with six volumes published between 1922 and 1937; the seventh and final volume was prepared for publication but appeared almost twenty years after Engel's death. He was also the editor of the collected works of Hermann Grassmann. Engel translated the works of Nikolai Lobachevski from Russian i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Stäckel
Paul Gustav Samuel Stäckel (20 August 1862, Berlin – 12 December 1919, Heidelberg) was a German mathematician, active in the areas of differential geometry, number theory, and non-Euclidean geometry. In the area of prime number theory, he used the term ''twin prime'' (in its German form, "Primzahlzwilling") for the first time. After passing his ''Abitur'' in 1880 he studied mathematics and physics at the University of Berlin, but also listened to lectures on philosophy, psychology, education, and history. A year later he qualified for teaching in higher education and then taught at ''Gymnasien'' in Berlin. In 1885 he wrote his doctoral dissertation under Leopold Kronecker and Karl Weierstraß. In 1891 he completed his ''Habilitation'' at the University of Halle. Later he worked as a professor at the University of Königsberg (''außerordentlicher Professor'' from 1895 to 1897), the University of Kiel (''ordentlicher Professor'', 1897 to 1905), University of Hannover (1905 to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Function
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the unit hyperbola. Also, similarly to how the derivatives of and are and respectively, the derivatives of and are and respectively. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. They also occur in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics, including electromagnetic theory, heat transfer, fluid dynamics, and special relativity. The basic hyperbolic functions are: * hyperbolic sine "" (), * hyperbolic cosine "" (),''Collins Concise Dictionary'', p. 328 from which are derived: * hyperbolic tangent "" (), * hyp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
