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Carl Anton Bretschneider
Carl Anton Bretschneider (27 May 1808 – 6 November 1878) was a mathematician from Gotha, Germany. Bretschneider worked in geometry, number theory, and history of geometry. He also worked on logarithmic integrals and mathematical tables. He was one of the first mathematicians to use the symbol \gamma for Euler's constant when he published his 1837 paper. He is best known for his discovery of Bretschneider's formula for the area of a general quadrilateral on a plane, A = \sqrt , where, a, b, c, and d are the sides of the quadrilateral, s = \frac is the semiperimeter, and \alpha and \gamma are two opposite angles. He is the son of Karl Gottlieb Bretschneider, a theologian. Publications *Carl Anton Bretschneider (1837). "Theoriae logarithmi integralis lineamenta nova". Crelle Journal, vol.17, p. 257-285 (submitted 1835) See also * Heron's formula * Brahmagupta's formula References *Leonard Eugene Dickson Leonard Eugene Dickson (January 22, 1874 – January ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuadrilátero 06
''Cuadrilátero '' ( en, Boxing ring) is a 1970 Spanish boxing-themed film directed by Eloy de la Iglesia and starring José María Prada, Deane Selmier and Rosana Yanny. Cast *Dean Selmier as Miguel Valdés * José Legra as José Laguna *Rosanna Yanni as Elena *José María Prada José María Prada Oterino (31 March 1925 – 13 August 1978) was a Spanish film and television actor. He appeared in more than 80 films and television shows between 1954 and 1978. Partial filmography * ''Comedians'' (1954) - Decorador * ... *Irene Daina as Olga *María Luisa San José as prostitute *Pilar Cansino as Estrella References External links * 1970 films Films directed by Eloy de la Iglesia 1970s Spanish-language films Spanish boxing films 1970s Spanish films {{1970s-Spain-film-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semiperimeter
In geometry, the semiperimeter of a polygon is half its perimeter. Although it has such a simple derivation from the perimeter, the semiperimeter appears frequently enough in formulas for triangles and other figures that it is given a separate name. When the semiperimeter occurs as part of a formula, it is typically denoted by the letter ''s''. Triangles The semiperimeter is used most often for triangles; the formula for the semiperimeter of a triangle with side lengths ''a'', ''b'', and ''c'' is :s = \frac. Properties In any triangle, any vertex and the point where the opposite excircle touches the triangle partition the triangle's perimeter into two equal lengths, thus creating two paths each of which has a length equal to the semiperimeter. If A, B, C, A', B', and C' are as shown in the figure, then the segments connecting a vertex with the opposite excircle tangency (AA', BB', and CC', shown in red in the diagram) are known as splitters, and s = , AB, +, A'B, =, AB, +, AB' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1808 Births
Eighteen or 18 may refer to: * 18 (number), the natural number following 17 and preceding 19 * one of the years 18 BC, AD 18, 1918, 2018 Film, television and entertainment * ''18'' (film), a 1993 Taiwanese experimental film based on the short story ''God's Dice'' * ''Eighteen'' (film), a 2005 Canadian dramatic feature film * 18 (British Board of Film Classification), a film rating in the United Kingdom, also used in Ireland by the Irish Film Classification Office * 18 (''Dragon Ball''), a character in the ''Dragon Ball'' franchise * "Eighteen", a 2006 episode of the animated television series ''12 oz. Mouse'' Music Albums * ''18'' (Moby album), 2002 * ''18'' (Nana Kitade album), 2005 * '' 18...'', 2009 debut album by G.E.M. Songs * "18" (5 Seconds of Summer song), from their 2014 eponymous debut album * "18" (One Direction song), from their 2014 studio album ''Four'' * "18", by Anarbor from their 2013 studio album '' Burnout'' * "I'm Eighteen", by Alice Cooper common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19th-century German Mathematicians
The 19th (nineteenth) century began on 1 January 1801 ( MDCCCI), and ended on 31 December 1900 ( MCM). The 19th century was the ninth century of the 2nd millennium. The 19th century was characterized by vast social upheaval. Slavery was abolished in much of Europe and the Americas. The First Industrial Revolution, though it began in the late 18th century, expanding beyond its British homeland for the first time during this century, particularly remaking the economies and societies of the Low Countries, the Rhineland, Northern Italy, and the Northeastern United States. A few decades later, the Second Industrial Revolution led to ever more massive urbanization and much higher levels of productivity, profit, and prosperity, a pattern that continued into the 20th century. The Islamic gunpowder empires fell into decline and European imperialism brought much of South Asia, Southeast Asia, and almost all of Africa under colonial rule. It was also marked by the collapse of the large S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonard Eugene Dickson
Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also remembered for a three-volume history of number theory, ''History of the Theory of Numbers''. Life Dickson considered himself a Texan by virtue of having grown up in Cleburne, where his father was a banker, merchant, and real estate investor. He attended the University of Texas at Austin, where George Bruce Halsted encouraged his study of mathematics. Dickson earned a B.S. in 1893 and an M.S. in 1894, under Halsted's supervision. Dickson first specialised in Halsted's own specialty, geometry.A. A. Albert (1955Leonard Eugene Dickson 1874–1954from National Academy of Sciences Both the University of Chicago and Harvard University welcomed Dickson as a Ph.D. student, and Dickson initially accepted Harvard's offer, but chose to attend Chicago in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brahmagupta's Formula
In Euclidean geometry, Brahmagupta's formula is used to find the area of any cyclic quadrilateral (one that can be inscribed in a circle) given the lengths of the sides; its generalized version (Bretschneider's formula) can be used with non-cyclic quadrilateral. Heron's formula can be thought as a sub-case of the Brahmagupta's formula. Formula Brahmagupta's formula gives the area of a cyclic quadrilateral whose sides have lengths , , , as : K=\sqrt where , the semiperimeter, is defined to be : s=\frac. This formula generalizes Heron's formula for the area of a triangle. A triangle may be regarded as a quadrilateral with one side of length zero. From this perspective, as approaches zero, a cyclic quadrilateral converges into a cyclic triangle (all triangles are cyclic), and Brahmagupta's formula simplifies to Heron's formula. If the semiperimeter is not used, Brahmagupta's formula is : K=\frac\sqrt. Another equivalent version is : K=\frac\cdot Proof Trigonometric p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heron's Formula
In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths , , . If s = \tfrac12(a + b + c) is the semiperimeter of the triangle, the area is, :A = \sqrt. It is named after first-century engineer Heron of Alexandria (or Hero) who proved it in his work ''Metrica'', though it was probably known centuries earlier. Example Let be the triangle with sides , and . This triangle’s semiperimeter is :s=\frac=\frac=16 and so the area is : \begin A &= \sqrt = \sqrt\\ &= \sqrt = \sqrt = 24. \end In this example, the side lengths and area are integers, making it a Heronian triangle. However, Heron's formula works equally well in cases where one or more of the side lengths are not integers. Alternate expressions Heron's formula can also be written in terms of just the side lengths instead of using the semiperimeter, in several ways, :\begin A &=\tfrac\sqrt \\ mu&=\tfrac\sqrt \\ mu&=\tfrac\sqrt \\ mu&=\tfrac\sqrt \\ mu&=\tfra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Gottlieb Bretschneider
Karl Gottlieb Bretschneider (February 11, 1776 in Gersdorf, Saxony – January 22, 1848 in Gotha, Thuringia) was a German Protestant scholar and theologian from Gersdorf, Saxony. He is noted for, among other things, having planned and founded the monumental '' Corpus Reformatorum''. He is the father of Carl Anton Bretschneider, a mathematician. In 1794, he entered the University of Leipzig, where he studied theology for four years. After some years of hesitation he resolved to be ordained, and in 1802 he passed with great distinction the examination for candidatus theologiae, and attracted the regard of Franz Volkmar Reinhard (1753–1812), author of the ''System der christlichen Moral'' (1788–1815), then court-preacher at Dresden, who became his warm friend and patron during the remainder of his life. From 1804 to 1806, Bretschneider was '' Privatdozent'' at the University of Wittenberg, where he lectured on philosophy and theology. During this time he wrote his work on the d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bretschneider's Formula
In geometry, Bretschneider's formula is the following expression for the area of a general quadrilateral: : K = \sqrt ::= \sqrt . Here, , , , are the sides of the quadrilateral, is the semiperimeter, and and are any two opposite angles, since \cos (\alpha+ \gamma) = \cos (\beta+ \delta) as long as \alpha+\beta+\gamma+\delta=360^. Bretschneider's formula works on both convex and concave quadrilaterals (but not crossed ones), whether it is cyclic or not. The German mathematician Carl Anton Bretschneider discovered the formula in 1842. The formula was also derived in the same year by the German mathematician Karl Georg Christian von Staudt. Proof Denote the area of the quadrilateral by . Then we have : \begin K &= \frac + \frac.\end Therefore : 2K= (ad) \sin \alpha + (bc) \sin \gamma. : 4K^2 = (ad)^2 \sin^2 \alpha + (bc)^2 \sin^2 \gamma + 2abcd \sin \alpha \sin \gamma. The law of cosines implies that : a^2 + d^2 -2ad \cos \alpha = b^2 + c^2 -2bc \cos \gamma, because bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gotha (town)
Gotha () is the fifth-largest city in Thuringia, Germany, west of Erfurt and east of Eisenach with a population of 44,000. The city is the capital of the district of Gotha and was also a residence of the Ernestine Wettins from 1640 until the end of monarchy in Germany in 1918. The House of Saxe-Coburg and Gotha originating here spawned many European rulers, including the royal houses of the United Kingdom, Belgium, Portugal (until 1910) and Bulgaria (until 1946). In the Middle Ages, Gotha was a rich trading town on the trade route ''Via Regia'' and between 1650 and 1850, Gotha saw a cultural heyday as a centre of sciences and arts, fostered by the dukes of Saxe-Gotha. The first duke, Ernest the Pious, was famous for his wise rule. In the 18th century, the ''Almanach de Gotha'' was first published in the city. The publisher Justus Perthes and the encyclopedist Joseph Meyer made Gotha a leading centre of German publishing around 1800. In the early 19th century, Gotha was a bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Constant
Euler's constant (sometimes also called the Euler–Mascheroni constant) is a mathematical constant usually denoted by the lowercase Greek letter gamma (). It is defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by \log: :\begin \gamma &= \lim_\left(-\log n + \sum_^n \frac1\right)\\ px&=\int_1^\infty\left(-\frac1x+\frac1\right)\,dx. \end Here, \lfloor x\rfloor represents the floor function. The numerical value of Euler's constant, to 50 decimal places, is: : History The constant first appeared in a 1734 paper by the Swiss mathematician Leonhard Euler, titled ''De Progressionibus harmonicis observationes'' (Eneström Index 43). Euler used the notations and for the constant. In 1790, Italian mathematician Lorenzo Mascheroni used the notations and for the constant. The notation appears nowhere in the writings of either Euler or Mascheroni, and was chosen at a later time perhaps because of the constant's connect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
