|
Frederick S. Woods
Frederick Shenstone Woods (1864–1950) was an American mathematician. He was a part of the mathematics faculty of the Massachusetts Institute of Technology from 1895 to 1934, being head of the department of mathematics from 1930 to 1934 and chairman of the MIT faculty from 1931 to 1933. His textbook on analytic geometry in 1897 was reviewed by Maxime Bocher. In 1901 he wrote on Riemannian geometry and curvature of Riemannian manifolds. In 1903 he spoke on non-Euclidean geometry. Works * 1901: * 1905: * 1907: (with Frederick H. Bailey) A course in mathematics' via Internet Archive * 1917: (with Frederick H. Bailey) Analytic geometry and calculus' via Internet Archive * 1922: (with Frederick H. Bailey) Elementary calculus' via Internet Archive * 1922: Higher geometry' Non-Euclidean geometry Following Wilhelm Killing (1885) and others, Woods described motions in spaces of non-Euclidean geometry in the form: :x_^=x_\cos kl+x_\frac,\quad x_^=x_,\quad x_^=x_,\quad x_^=-x_k\sin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Americans
Americans are the Citizenship of the United States, citizens and United States nationality law, nationals of the United States, United States of America.; ; Although direct citizens and nationals make up the majority of Americans, many Multiple citizenship, dual citizens, expatriates, and green card, permanent residents could also legally claim American nationality. The United States is home to race and ethnicity in the United States, people of many racial and ethnic origins; consequently, culture of the United States, American culture and Law of the United States, law do not equate nationality with Race (human categorization), race or Ethnic group, ethnicity, but with citizenship and an Oath of Allegiance (United States), oath of permanent allegiance. Overview The majority of Americans or their ancestors Immigration to the United States, immigrated to the United States or are descended from people who were Trans Atlantic Slave Trade, brought as Slavery in the United States ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-Euclidean Geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed, then there are affine planes associated with the planar algebras, which give rise to kinematic geometries that have also been called non-Euclidean geometry. The essential difference between the metric geometries is the nature of parallel lines. Euclid's fifth postulate, the parallel postulate, is equivalent to Playfair's postulate, which states that, within a two-dimensional plane, for any given line and a point ''A'', which is not on , there is exactly one line through ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematicians From Massachusetts
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1950 Deaths
Year 195 ( CXCV) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Scrapula and Clemens (or, less frequently, year 948 ''Ab urbe condita''). The denomination 195 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Emperor Septimius Severus has the Roman Senate deify the previous emperor Commodus, in an attempt to gain favor with the family of Marcus Aurelius. * King Vologases V and other eastern princes support the claims of Pescennius Niger. The Roman province of Mesopotamia rises in revolt with Parthian support. Severus marches to Mesopotamia to battle the Parthians. * The Roman province of Syria is divided and the role of Antioch is diminished. The Romans annexed the Syrian cities of Edessa and Nisibis. Severus re-establish his he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1864 Births
Events January–March * January 13 – American songwriter Stephen Foster ("Oh! Susanna", "Old Folks at Home") dies aged 37 in New York City, leaving a scrap of paper reading "Dear friends and gentle hearts". His parlor song " Beautiful Dreamer" is published in March. * January 16 – Denmark rejects an Austrian-Prussian ultimatum to repeal the Danish Constitution, which says that Schleswig-Holstein is part of Denmark. * January 21 – New Zealand Wars: The Tauranga campaign begins. * February – John Wisden publishes '' The Cricketer's Almanack for the year 1864'' in England; it will go on to become the major annual cricket reference publication. * February 1 – Danish-Prussian War (Second Schleswig War): 57,000 Austrian and Prussian troops cross the Eider River into Denmark. * February 15 – Heineken brewery founded in Netherlands. * February 17 – American Civil War: The tiny Confederate hand-propelled submarine ''H. L. Hunl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Boost
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the Dutch physicist Hendrik Lorentz. The most common form of the transformation, parametrized by the real constant v, representing a velocity confined to the -direction, is expressed as \begin t' &= \gamma \left( t - \frac \right) \\ x' &= \gamma \left( x - v t \right)\\ y' &= y \\ z' &= z \end where and are the coordinates of an event in two frames with the origins coinciding at 0, where the primed frame is seen from the unprimed frame as moving with speed along the -axis, where is the speed of light, and \gamma = \left ( \sqrt\right )^ is the Lorentz factor. When speed is much smaller than , the Lorentz factor is negligibly different from 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilhelm Killing
Wilhelm Karl Joseph Killing (10 May 1847 – 11 February 1923) was a German mathematician who made important contributions to the theories of Lie algebras, Lie groups, and non-Euclidean geometry. Life Killing studied at the University of Münster and later wrote his dissertation under Karl Weierstrass and Ernst Kummer at Berlin in 1872. He taught in gymnasia (secondary schools) from 1868 to 1872. He became a professor at the seminary college Collegium Hosianum in Braunsberg (now Braniewo). He took holy orders in order to take his teaching position. He became rector of the college and chair of the town council. As a professor and administrator Killing was widely liked and respected. Finally, in 1892 he became professor at the University of Münster. In 1886, Killing and his spouse entered the Third Order of Franciscans. Work In 1878 Killing wrote on space forms in terms of non-Euclidean geometry in Crelle's Journal, which he further developed in 1880 as well as in 1885. Re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, movies/videos, moving images, and millions of books. In addition to its archiving function, the Archive is an activist organization, advocating a free and open Internet. , the Internet Archive holds over 35 million books and texts, 8.5 million movies, videos and TV shows, 894 thousand software programs, 14 million audio files, 4.4 million images, 2.4 million TV clips, 241 thousand concerts, and over 734 billion web pages in the Wayback Machine. The Internet Archive allows the public to upload and download digital material to its data cluster, but the bulk of its data is collected automatically by its web crawlers, which work to preserve as much of the public web as possible. Its web archiving, web archive, the Wayback Machine, contains hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The 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] |
Curvature Of Riemannian Manifolds
In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension greater than 2 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous way to define curvature for these manifolds, now known as the Riemann curvature tensor. Similar notions have found applications everywhere in differential geometry. For a more elementary discussion see the article on curvature which discusses the curvature of curves and surfaces in 2 and 3 dimensions, as well as the differential geometry of surfaces. The curvature of a pseudo-Riemannian manifold can be expressed in the same way with only slight modifications. Ways to express the curvature of a Riemannian manifold The Riemann curvature tensor The curvature of a Riemannian manifold can be described in various ways; the most standard one is the curvature tensor, given in terms of a Levi-Civita connection (or covariant differentiatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemannian Geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a ''Riemannian metric'', i.e. with an inner product on the tangent space at each point that varies smoothly from point to point. This gives, in particular, local notions of angle, length of curves, surface area and volume. From those, some other global quantities can be derived by integrating local contributions. Riemannian geometry originated with the vision of Bernhard Riemann expressed in his inaugural lecture "''Ueber die Hypothesen, welche der Geometrie zu Grunde liegen''" ("On the Hypotheses on which Geometry is Based.") It is a very broad and abstract generalization of the differential geometry of surfaces in R3. Development of Riemannian geometry resulted in synthesis of diverse results concerning the geometry of surfaces and the behavior of geodesics on them, with techniques that can be applied to the study of differentiable manifolds of higher dim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
