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Nikolai Lobachevski
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 Bre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lobachevsky (other)
Nikolai Lobachevsky (1792–1856) was a Russian mathematician. Lobachevsky (Лобачевский ; also Lobachevskij and Lobachevskiy; feminine: Lobachevskaya), a Russian-language surname, may also refer to: * 1858 Lobachevskij, a main-belt asteroid * N. I. Lobachevsky State University of Nizhny Novgorod or Lobachevsky University, Novgorod Oblast, Russia * Lobachevskiy (crater), a crater on the moon * Lobachevsky Prize The Lobachevsky Prize, awarded by the Russian Academy of Sciences, and the Lobachevsky Medal, awarded by the Kazan State University, are mathematical awards in honor of Nikolai Ivanovich Lobachevsky. History The Lobachevsky Prize was established ..., including the Lobachevsky Medal * Lobachevsky function, also called the Clausen function * "Lobachevsky" (song), a humorous song by Tom Lehrer * Lobachevskian or hyperbolic geometry See also * Łobaczewski (surname), the Polish-language equivalent of the surname {{Disambig, surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lobachevskian Geometry
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai– Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P'' not on ''R'', in the plane containing both line ''R'' and point ''P'' there are at least two distinct lines through ''P'' that do not intersect ''R''. (Compare the above with Playfair's axiom, the modern version of Euclid's parallel postulate.) Hyperbolic plane geometry is also the geometry of pseudospherical surfaces, surfaces with a constant negative Gaussian curvature. Saddle surfaces have negative Gaussian curvature in at least some regions, where they locally resemble the hyperbolic plane. A modern use of hyperbolic geometry is in the theory of special relativity, particularly the Minkowski model. When geometers first realised they were working with something other than the standard Euclidean geometry, they described their geomet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poles
Poles,, ; singular masculine: ''Polak'', singular feminine: ''Polka'' or Polish people, are a West Slavic nation and ethnic group, who share a common history, culture, the Polish language and are identified with the country of Poland in Central Europe. The preamble to the Constitution of the Republic of Poland defines the Polish nation as comprising all the citizens of Poland, regardless of heritage or ethnicity. The majority of Poles adhere to Roman Catholicism. The population of self-declared Poles in Poland is estimated at 37,394,000 out of an overall population of 38,512,000 (based on the 2011 census), of whom 36,522,000 declared Polish alone. A wide-ranging Polish diaspora (the '' Polonia'') exists throughout Europe, the Americas, and in Australasia. Today, the largest urban concentrations of Poles are within the Warsaw and Silesian metropolitan areas. Ethnic Poles are considered to be the descendants of the ancient West Slavic Lechites and other tribes that inhabi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid
Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved new innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus (mathematician), Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics. Very little is known of Euclid's life, and most information comes from the philosophers Proclus and Pappus of Alexandria many centuries later. Until the early Renaissance he was often mistaken f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemy
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importance to later Byzantine, Islamic, and Western European science. The first is the astronomical treatise now known as the '' Almagest'', although it was originally entitled the ''Mathēmatikē Syntaxis'' or ''Mathematical Treatise'', and later known as ''The Greatest Treatise''. The second is the ''Geography'', which is a thorough discussion on maps and the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the ''Apotelesmatika'' (lit. "On the Effects") but more commonly known as the '' Tetrábiblos'', from the Koine Greek meaning "Four Books", or by its Latin equivalent ''Quadrip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galen
Aelius Galenus or Claudius Galenus ( el, Κλαύδιος Γαληνός; September 129 – c. AD 216), often Anglicized as Galen () or Galen of Pergamon, was a Greek physician, surgeon and philosopher in the Roman Empire. Considered to be one of the most accomplished of all medical researchers of antiquity, Galen influenced the development of various scientific disciplines, including anatomy, physiology, pathology, pharmacology, and neurology, as well as philosophy and logic. The son of Aelius Nicon, a wealthy Greek architect with scholarly interests, Galen received a comprehensive education that prepared him for a successful career as a physician and philosopher. Born in the ancient city of Pergamon (present-day Bergama, Turkey), Galen traveled extensively, exposing himself to a wide variety of medical theories and discoveries before settling in Rome, where he served prominent members of Roman society and eventually was given the position of personal physician to several emp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vesalius
Andreas Vesalius (Latinized from Andries van Wezel) () was a 16th-century anatomist, physician, and author of one of the most influential books on human anatomy, ''De Humani Corporis Fabrica Libri Septem'' (''On the fabric of the human body'' ''in seven books''). Vesalius is often referred to as the founder of modern human anatomy. He was born in Brussels, which was then part of the Habsburg Netherlands. He was a professor at the University of Padua (1537–1542) and later became Imperial physician at the court of Emperor Charles V. ''Andreas Vesalius'' is the Latinized form of the Dutch name Andries van Wesel. It was a common practice among European scholars in his time to Latinize their names. His name is also given as ''Andrea Vesalius'', ''André Vésale'', ''Andrea Vesalio'', ''Andreas Vesal'', ''Andrés Vesalio'' and ''Andre Vesale''. Early life and education Vesalius was born as Andries van Wesel to his father Anders van Wesel and mother Isabel Crabbe on 31 December 151 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Copernicus
Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulated a model of the universe that placed the Sun rather than Earth at its center. In all likelihood, Copernicus developed his model independently of Aristarchus of Samos, an ancient Greek astronomer who had formulated such a model some eighteen centuries earlier. The publication of Copernicus's model in his book ' (''On the Revolutions of the Celestial Spheres''), just before his death in 1543, was a major event in the history of science, triggering the Copernican Revolution and making a pioneering contribution to the Scientific Revolution. Copernicus was born and died in Royal Prussia, a region that had been part of the Kingdom of Poland since 1466. A polyglot and polymath, he obtained a doctorate in canon law and was a mathematician, astro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Kingdon Clifford
William Kingdon Clifford (4 May 18453 March 1879) was an English mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour. The operations of geometric algebra have the effect of mirroring, rotating, translating, and mapping the geometric objects that are being modelled to new positions. Clifford algebras in general and geometric algebra in particular have been of ever increasing importance to mathematical physics, geometry, and computing. Clifford was the first to suggest that gravitation might be a manifestation of an underlying geometry. In his philosophical writings he coined the expression ''mind-stuff''. Biography Born at Exeter, England, Exeter, William Clifford showed great promise at school. He went on to King's College London (at age 15) and Trinity College, Cambridge, where he was elected fellow in 1868, after being second Wrangler (Universi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lobachevsky Integral Formula
In mathematics, Dirichlet integrals play an important role in distribution theory. We can see the Dirichlet integral in terms of distributions. One of those is the improper integral of the sinc function over the positive real line, : \int_0^\infty \frac x \, dx =\int_0^\infty \frac \, dx = \frac \pi 2. Lobachevsky's Dirichlet integral formula Let f(x) be a continuous function satisfying the \pi-periodic assumption f(x+\pi)=f(x), and f(\pi-x)=f(x), for 0\leq x<\infty. If the is taken to be an , we have |
Dirichlet Integrals
In mathematics, there are several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral of the sinc function over the positive real line: : \int_0^\infty \frac \,dx = \frac. This integral is not absolutely convergent, meaning \Biggl, \frac \Biggl, is not Lebesgue-integrable, and so the Dirichlet integral is undefined in the sense of Lebesgue integration. It is, however, defined in the sense of the improper Riemann integral or the generalized Riemann or Henstock–Kurzweil integral. This can be seen by using Dirichlet's test for improper integrals. Although the sine integral, an antiderivative of the sinc function, is not an elementary function, the value of the integral (in the Riemann or Henstock sense) can be derived using various ways, including the Laplace transform, double integration, differentiating under the integral sign, contour integration, and the Dirichlet kernel. Evalu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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