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Peano Surface
In mathematics, the Peano surface is the graph of the two-variable function :f(x,y)=(2x^2-y)(y-x^2). It was proposed by Giuseppe Peano in 1899 as a counterexample to a conjectured criterion for the existence of maxima and minima of functions of two variables. The surface was named the Peano surface (german: Peanosche Fläche) by Georg Scheffers in his 1920 book ''Lehrbuch der darstellenden Geometrie''. It has also been called the Peano saddle. See especially section "Peano Saddle", pp. 562–563. Properties The function f(x,y)=(2x^2-y)(y-x^2) whose graph is the surface takes positive values between the two parabolas y=x^2 and y=2x^2, and negative values elsewhere (see diagram). At the origin, the three-dimensional point (0,0,0) on the surface that corresponds to the intersection point of the two parabolas, the surface has a saddle point. The surface itself has positive Gaussian curvature in some parts and negative curvature in others, separated by another parabola, implying th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modell Einer Peanoschen Fläche -Schilling XLIX, 1-
Modell is the German word for "model" and also a surname. It may refer to: People * Arnold Modell (1924–2022), American professor of social psychiatry * Art Modell (1925–2012), American business executive and sports team owner * Bernadette Modell, (born 1935), British geneticist * David Modell (1961–2017), American business executive and sports team owner * Frank Modell (1917-2016), American cartoonist * Merriam Modell (1908–1994), American author of pulp fiction * Pat Modell (1931–2011), American TV actress * Rod Modell, given name for Deepchord, electronic music producer from Detroit, Michigan * William Modell (1921–2008), American businessman and chairman of Modell's Sporting Goods Companies * Modell's, a sporting goods retailer based in New York City * Modell (pawn shop), a pawnbroker based in New York City, originally formed as a spinoff of the sporting goods company * Schabak Modell, a die-cast toy producer in Germany * Schuco Modell, a die-cast toy producer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fighting occurring throughout Europe, the Middle East, Africa, the Pacific, and parts of Asia. An estimated 9 million soldiers were killed in combat, plus another 23 million wounded, while 5 million civilians died as a result of military action, hunger, and disease. Millions more died in genocides within the Ottoman Empire and in the 1918 influenza pandemic, which was exacerbated by the movement of combatants during the war. Prior to 1914, the European great powers were divided between the Triple Entente (comprising France, Russia, and Britain) and the Triple Alliance (containing Germany, Austria-Hungary, and Italy). Tensions in the Balkans came to a head on 28 June 1914, following the assassination of Archduke Franz Ferdin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TU Dresden
TU Dresden (for german: Technische Universität Dresden, abbreviated as TUD and often wrongly translated as "Dresden University of Technology") is a public research university, the largest institute of higher education in the city of Dresden, the largest university in Saxony and one of the 10 largest universities in Germany with 32,389 students . The name Technische Universität Dresden has only been used since 1961; the history of the university, however, goes back nearly 200 years to 1828. This makes it one of the oldest colleges of technology in Germany, and one of the country’s oldest universities, which in German today refers to institutes of higher education that cover the entire curriculum. The university is a member of TU9, a consortium of the nine leading German Institutes of Technology. The university is one of eleven German universities which succeeded in the Excellence Initiative in 2012, thus getting the title of a "University of Excellence". The TU Dresden succee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Göttingen
The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded in 1734 by George II, King of Great Britain and Elector of Hanover, and starting classes in 1737, the Georgia Augusta was conceived to promote the ideals of the Enlightenment. It is the oldest university in the state of Lower Saxony and the largest in student enrollment, which stands at around 31,600. Home to many noted figures, it represents one of Germany's historic and traditional institutions. According to an official exhibition held by the University of Göttingen in 2002, 44 Nobel Prize winners had been affiliated with the University of Göttingen as alumni, faculty members or researchers by that year alone. The University of Göttingen was previously supported by the German Universities Excellence Initiative, holds memberships ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ludwig Scheeffer
Karl Ludwig Scheeffer (born 1 June 1859 in Königsberg;Vita n Latinin his Ph.D. thesis, died 11 June 1885 in Munich) was a German mathematician and university teacher.''Ludwig Scheeffer'' (obituary by Georg Cantor), in: ''Bibliotheca mathematica'WS1885197–199/ref> Life Scheeffer's parents were the protestants Ludwig and Mathilda, née Broscheit. He first attended a Gymnasium in Königsberg and after his father's death transferred to the . In 1875, he was accepted at the Friedrich Wilhelm University of Berlin, where he studied for four years, except two semesters at Heidelberg and Leipzig. On 1 March 1880, he finally received his doctorate from the University of Berlin with the dissertation ''"Ueber Bewegungen starrer Punktsysteme in einer ebenen n-fachen Mannigfaltigkeit (On motions of rigid point systems in a plane n-fold manifold)"''. Since initially he did not strive for a university career, he passed the necessary examination for the teaching profession in the subjects ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus and integral calculus; the former concerns instantaneous Rate of change (mathematics), rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence (mathematics), convergence of infinite sequences and Series (mathematics), infinite series to a well-defined limit (mathematics), limit. Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Later work, including (ε, δ)-definition of limit, codify ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angelo Genocchi
Angelo Genocchi (5 March 1817 – 7 March 1889) was an Italian mathematician who specialized in number theory. He worked with Giuseppe Peano. The Genocchi number In mathematics, the Genocchi numbers G''n'', named after Angelo Genocchi, are a sequence of integers that satisfy the relation : \frac=\sum_^\infty G_n\frac The first few Genocchi numbers are 0, −1, −1, 0, 1, 0, −3, 0, 17 , se ...s are named after him. Genocchi was President of the Academy of Sciences of Turin. Notes References * Obituary in: * 19th-century Italian mathematicians 1817 births 1889 deaths {{Italy-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous Polynomial
In mathematics, a homogeneous polynomial, sometimes called quantic in older texts, is a polynomial whose nonzero terms all have the same degree. For example, x^5 + 2 x^3 y^2 + 9 x y^4 is a homogeneous polynomial of degree 5, in two variables; the sum of the exponents in each term is always 5. The polynomial x^3 + 3 x^2 y + z^7 is not homogeneous, because the sum of exponents does not match from term to term. The function defined by a homogeneous polynomial is always a homogeneous function. An algebraic form, or simply form, is a function defined by a homogeneous polynomial. A binary form is a form in two variables. A ''form'' is also a function defined on a vector space, which may be expressed as a homogeneous function of the coordinates over any basis. A polynomial of degree 0 is always homogeneous; it is simply an element of the field or ring of the coefficients, usually called a constant or a scalar. A form of degree 1 is a linear form. A form of degree 2 is a quadratic fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Form
In mathematics, a cubic form is a homogeneous polynomial of degree 3, and a cubic hypersurface is the zero set of a cubic form. In the case of a cubic form in three variables, the zero set is a cubic plane curve. In , Boris Delone and Dmitry Faddeev showed that binary cubic forms with integer coefficients can be used to parametrize orders in cubic fields. Their work was generalized in to include all cubic rings (a is a ring that is isomorphic to Z3 as a Z-module),In fact, Pierre Deligne pointed out that the correspondence works over an arbitrary scheme. giving a discriminant-preserving bijection between orbits of a GL(2, Z)-action on the space of integral binary cubic forms and cubic rings up to isomorphism. The classification of real cubic forms a x^3 + 3 b x^2 y + 3 c x y^2 + d y^3 is linked to the classification of umbilical points of surfaces. The equivalence classes of such cubics form a three-dimensional real projective space and the subset of parabolic forms define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Form
In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, :4x^2 + 2xy - 3y^2 is a quadratic form in the variables and . The coefficients usually belong to a fixed field , such as the real or complex numbers, and one speaks of a quadratic form over . If K=\mathbb R, and the quadratic form takes zero only when all variables are simultaneously zero, then it is a definite quadratic form, otherwise it is an isotropic quadratic form. Quadratic forms occupy a central place in various branches of mathematics, including number theory, linear algebra, group theory (orthogonal group), differential geometry (Riemannian metric, second fundamental form), differential topology ( intersection forms of four-manifolds), and Lie theory (the Killing form). Quadratic forms are not to be confused with a quadratic equation, which has only one variable and includes terms of degree two or less. A quadratic form is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series, when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally better as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
