61. Club-Internet Encyclopédie Translate this page Titres (1-5 / 5) Günther (Hans F. K.) Günther (Ignaz) Günther (Matthäus) grassmann(hermann Günther) Kluge (Hans Günther von), le racisme Tous les mots http://www.club-internet.fr/cgi-bin/h?Günther

62. Evolution Of Geometric Algebra And Calculus Leibniz articulated the dream of a universal geometric calculus in the seventeenthcentury, its realization began in 1844 with hermann grassmann's great work http://modelingnts.la.asu.edu/html/Evolution.html

On the Evolution of Geometric Algebra and Geometric Calculus Though Leibniz articulated the dream of a universal geometric calculus in the seventeenth century, its realization began in 1844 with Hermann Grassmann's great work Die Lineale Ausdehnungslehre Grassmann's Vision was so far ahead of its time, however, that it took more than a century to be widely appreciated [Schubring, 1996]. In the meantime Grassmann penetrated deep into the thinking of such excellent mathematicians as Peano [ ] and Whitehead [ ], but their work failed to advance or promulgate his vision. Many of his ideas were rediscovered and/or further developed anonymously in various branches of mathematics, but without his unifying perspective. Grassmann's program to develop a universal geometric calculus reemerged in 1966 with the book Space-Time Algebra (STA) by David Hestenes, a refinement of his doctoral dissertation (UCLA, 1963). The idea of geometric algebra was given its modern form and reinvigorated by more than a century of advances in mathematics and physics since Grassmann. The main mathematical progenitors of Geometric Algebra (GA) and Geometric Calculus (GC) are shown in the Family Tree below. The roles of theoretical physics and the Lecture Notes of Marcel Riesz [

63. Worterbuch Zum Rig-Veda/Hermann Grassmann Worterbuch Zum RigVeda/hermann grassmann. Reprint. 1999, 1775 p.,ISBN 81-208-1636-6. grassmann's Worterbuch Zum Rig-Veda has http://www.vedamsbooks.com/no14539.htm

Worterbuch Zum Rig-Veda/Hermann Grassmann. Reprint. 1999, 1775 p., ISBN 81-208-1636-6. "Grassmann's "Worterbuch Zum Rig-Veda" has, even after more than 120 years of its publication in Leipzig in 1873, remained one of the most important tools for anyone who wishes to study the oldest Indian text in the original. It is complete, gives all the references even in the case of very common wordsalthough M. Kozianka, in the 6th revised and supplemented edition prepared by her (Wiesbaden, 1996), was able to add some references overlooked by G., takes the context into account, and contains even a reverse index. "Theslightlyidiosyncratic method of ignoring the traditional division of the text into mandalas and substituting for it a consecutive numbering of the suktas from 1 to 1017 may be a bit irritating, especially for the Indian reader, but this is a minor problem which can easily be over come, e.g. by entering Grassmann's numbers into one's own copy of the text or by using Geldner's translation as a concordance. A Major problem, however, is many of the meanings given by G. In this regard in particular the reader is strongly recommended to take into account the enormous progress achieved by Vedic scholars, even if these scholars do not fully agree with each other. But semantics is anyway one of the central problems of Sanskrit in general, not only of Vedic Sanskrit." (jacket) Return to Hinduism Catalogue

64. ¼¼°èÀÇ ¼öÇÐÀÚ Galilei, Galileo, Christian Goldbach. grassmann, hermann Gather, ?. Napier, John. http://math.dongeui.ac.kr/main/mathman/mathman_main.htm

KAIST ¼öÇаú TEL : (051) 890-1470 FAX : (051) 890-1470 Gauss, Karl Friedrich Goel, Kurt Galois, Evariste Gregory, James ... Christiaan Huygens

65. Fine Hall Library, Princeton University: New Books September 2000 2000, QA205 .G7413 2000, Extension Theory (History Of Mathematics Sources) vol. 19,grassmann, hermann. 2000, QA241 .R597 2000, A Course in padic Analysis, Springer. http://www.princeton.edu/~finelib/sep00bks.html

New Books (September 2000) Math or Physics Date of Publ Call Number Title Author Math Books... PRIN 865 2000 .2970 Flows on Graph DeVos, Matthew Jared Bashmakova, Isabella QA155 .H36 1996 vol.2 Handbook Of Algebra Hazewinkel, M. Physical Combinatorics Kashiwara, Masaki Basic Homological Algebra M. Scott Osborne Extension Theory (History Of Mathematics Sources) vol. 19 Grassmann, Hermann A Course in p-adic Analysis Springer Diophantine Approximation On Linear Algebraic Groups Michael Waldschmidt Euler Systems Rubin, Karl QA247 .R824 2000 c. 4 Euler Systems (Hermann Weyl Lectures The Institute for Advance Study Rubin, Karl QA3 .A572 ser. 2, vol. 198 On Dobrushin's Way From Probability Theory To Statistical Physics R.A. Minlos QA3 .L28 no. 1726 Regular Variation and Differential Equations Maric, Vojislav QA3 .L28 NO. 1727 Computing the Zeros of Analytic Functions Peter Kravanja QA3 .L28 no. 1728 Computer Algebra Methods For Equivariant Dynamical Systems Gatermann, Karin Singular Perturbations Of Differential Operators Albeverio, S. Hyperbolic Partial Differential Equations and Wave Phenomena Mitsuru Ikawa Optimization in Elliptic Problems with Applications to Mechanics of Deformable Bodies and Fluid Mechanics Litvinov, William G.

66. Untitled hermann grassmann (18091877) became a Sanskrit scholar, but in his sparetime turned to mathematical research because of his father's interests. http://members.fortunecity.com/jonhays/grassmann.htm

web hosting domain names email addresses related sites Elements was finally rewritten in arithmetic terminology by the father, to be developed by the son. Says Hestenes: "Hermann Grassmann completed the algebraic formulation of basic ideas in Greek ideas begun by Descartes. The Greek theory of ratio and proportion is now incorporated in the properties of scalar and vector multiplication. The Greek idea of projection is incorporated in the inner product. And the Greek geometrical product is expressed by outer multiplication. ....Only in ... Grassman's outer product is it possible to understand that the careful Greek distinction between number and magnitude as real geometric signigicance ... correspond[ing] roughly to the distinction between a scalar and a vector....Only in the work of Grassmann are the notions of direction, dimension, orientation and scalar magnitude finally disentangled ...impossible without the earlier vague distinction of the Greeks and perhaps without its reformulation in quasi-aruthmetic terms by his father....Grassmann was the first to define multiplication simply by specifying a set of algebraic rules." In the almost unreadable Ausdehninglehre (Calculus of Extension) , Grassmann built "a calculus of extensive magnitudes", a kind of vector algebraization of geometry , beginning with vector sum and difference . It's been said that Grassmann created many different kinds of vector products , but the notable ones are interior product (inner product), exterior product (related to outer product)

67. Hermann Gunther Grassmann Translate this page hermann grassmann fue un matemático brillante cuyas creaciones en elanálisis vectorial solo puede compararse con las de Hamilton. http://www.uaq.mx/matematicas/c2/cristinahis/hermann.html

HTTP 200 Document follows Date: Sat, 29 Mar 2003 18:41:01 GMT Server: NCSA/1.5.2 Last-modified: Fri, 06 Jul 2001 18:11:38 GMT Content-type: text/html Content-length: 3727 Hermann Gunther Grassman(1809-1877) Theorie der Ebbe und Flut Ausdehnungslehre , mismo que se convirtió en un clásico. Es un libro difícil de leer y contiene una gran parte del análisis vectorial moderno y hecho de tal forma que difícilmente puede resumirse. En el periodo de 1844 a 1861, Grassmann publicó 17 documentos científicos en los que se incluyen importantes documentos de física, varios sobre lenguas y libros de texto matemáticos. Editó un documento sobre política y también materiales sobre la evangelización de China. Este periodo de su vida terminó con su segundo Ausdehnungslehre . Después de 1862, Grassmann publicó un libro de texto en alemán y en latín sobre matemáticas, además de varios escritos sobre religión y sobre música así como un libro sobre terminología botánica alemana. También inventó el Heliostat de Grassmann. Esta combinación de actividades se debió a su creciente desacuerdo en la poca atención que recibían sus creaciones matemáticas.

68. Encyclopædia Britannica hermann grassmann and the Creation of Linear Algebra University of LeedsPaper analyzing the contributions of hermann grassmann to algebra. http://search.britannica.com/search?query=Hermann Goring

69. Aquí Matemàtiques: Enllaços D'interès. Història, Biografies, Obres Clàssiq Tasmania. hermann grassmann and the Creation of Linear Algebra a. hermanngrassmann and the Prehistory of Universal Algebra a. http http://www.xtec.es/recursos/mates/aqui/links/links_histbiog.htm

A Brief History of Algebra and Computing: An Eclectic Oxonian View Archimedes Biographies of Women Mathematicians Classical Works, Selecta and Opera Omnia ... The Mathematical Problems of David Hilbert Classical Works, Selecta and Opera Omnia http://www.emis.de/classics/index.html The Electronic Library of Mathematics a la web de The European Mathematical Information Service de la European Mathematical Society En aquest moment (gener del 2001) ja es poden consultar les obres de Bernhard Riemann i de Sir William Rowan Hamilton History of Mathematics http://aleph0.clarku.edu/~djoyce/mathhist/ A Brief History of Algebra and Computing: An Eclectic Oxonian View http://www.museums.reading.ac.uk/vmoc/algebra/ Jonathan Bowen , de la South Bank University Biographies of Women Mathematicians http://www.scottlan.edu/lriddle/women/women.htm Hypathia a Emmy Noether Mathematics. Ancient Science and Its Modern Fates http://www.ibiblio.org/expo/vatican.exhibit/exhibit/d-mathematics/Mathematics.html " "

70. Contents, Volume 7 as developed in Robert grassmann's Die Begriffslehre oder Logik Zweites Buch derFormenlehre oder Mathematik; and in such of hermann grassmann's works as the http://www.ed.ac.uk/philosophy/ml/abs7.html

Modern Logic Contents and abstracts for Modern Logic Volume 7 (1997) Vol. 7, no. 1 Vol. 7, no. 2 Vol. 7, nos. 3/4 Modern Logic 7 /1, January 1997 Irving ANELLIS John Vincent Atanasoff - His place in the history of computer logic and technology Modern Logic A brief sketch of Atanasoof's life is followed by an examination of his work at Iowa State University in construction of the ABC [Atanasoff-Berry Computer] electronic digital computer and an assessment of his role in the development of computer logic and technology, with emphasis in particular on his historical place in the theoretical and practical aspects of modern computer technology. Atanasoff envisioned the use of binary arithmetic for computation and Boolean switching-relay circuitry for machine logic, and the use of electronic and electrical components for machine hardware. Atanasoff and his student Clifford Berry completed construction of a working prototype of their machine in 1940, but failed to secure a patent for their work. John Mauchly visited Atanasoff in 1941 and examined the ABC, and with John Prespert Eckerd built ENIAC using the same logical and engineering principles which had been used in constructing the ABC. In discussing the historical background and context of Atanasoff's work, a greater emphasis is given to the lesser known work of Russian computer pioneers than is normally found in English historical surveys. Atanasoff himself was probably not aware of the historical background within which he worked.

71. Grassman Randy Rausch. hermann Günter grassmann. hermann grassmann is chieflyremembered for his development of a general calculus for vectors. http://panda.cs.ndsu.nodak.edu/~rausch/grassman.htm

Randy Rausch Hermann Günter Grassmann Born: April 15, 1808 in Stettin, Prussia (now Szczecin, Poland) Died: Sept 26, 1877 in Stettin, Germany (now Szczecin, Poland) Hermann Grassmann is chiefly remembered for his development of a general calculus for vectors. Grassmann taught at the Gymnasium in Stettin from 1831 until his death except for two years (1834-1836) when he taught in Berlin. Grassmann's most important work is Die lineale Ausdehnundslehre, ein neuer Zweig der Mathematik (1844) developed the idea of an algebra in which the symbols representing geometric entities such as points, lines and planes, are manipulated using certain rules. He represented subspaces of a space by coordinates leading to point mapping of an algebraic manifold now called the Grassmannian. Grassmann's methods were slow to be adopted but eventually they inspired the work of Élie Cartan and have since been used in studying differential forms and their application to analysis and geometry. Grassmann wrote on many other subjects, for example electricity, color, acoustics, linguistics and botany. At the age of 53 he became disappointed with the lack of interest in his mathematical ideas so he turned to Sanskrit studies, another of his interests. His Sanskrit dictionary is still widely used. Back to Mathematicians Back to My Essays Back to RandyLand

72. À¯¸íÇÑ ¼öÇÐÀÚ 21~1936.11.25) Guldberg, Cato Maximilian (1836.8.11~1902.1.14) grassmann, hermann Guther (1809.4.15~1877.9.26) Gregory http://user.chollian.net/~jjang88/mathman/mathman.htm

73. Read This: Briefly Noted hermann grassmann's Extension Theory (Ausdehnungslehre), first publishedin 1862, is a legendary book in the history of mathematics. http://www.maa.org/reviews/brief_may00.html

Read This! The MAA Online book review column Briefly Noted May 2000 New technologies create new possibilities. Early in 1999, John B. Cosgrave, using off-the-shelf mathematical software and mathematical ideas due to H. C. Pocklington, found a prime number with exactly 2000 digits. With the year 2000 on the horizon, it was inevitable that the number of digits would be related to the millennium. Cosgrave himself called it his "millennium prime," and its discovery garnered him some attention. For example, Ivars Peterson mentioned it in one of his MathTrek columns Excited by his discovery, Cosgrave wrote a long email message to his niece and nephew explaining some of the ideas that led to the discovery of the millennium prime. This email message now forms the major portion of the booklet A Prime for the Millennium , published by Folding Landscapes Press in Ireland. The booklet is charming, the story well told, and profits from the sales go to the Irish Cancer Society. Not a bad deal at all; check it out. (Fernando Q. Gouvêa)

74. Jean-Luc Dorier Translate this page EduMath 6, 38-48. Dorier JL (1997) hermann grassmann et la théoriede l'extension, Repères 26, 89-108. Dorier JL (1996) Genèse http://www-leibniz.imag.fr/DDM/PagesPerso/Dorier.html

Jean-Luc Dorier Email : Jean-Luc.Dorier@imag.fr Adresse postale : THESES H D iriger des R http://www-leibniz.imag.fr/LesCahiers/index.html - Grenoble 1 - 29 Juin 1990. ARTICLES DANS DES REVUES A COMITE DE LECTURE Dorier J.-L., Robert A., Robinet J., Rogalski M. (2000) On a research program about the teaching and learning of linear algebra in first year of French science university, International Journal of Mathematical Education in Sciences and Technology 31(1), 27-35. Dorier J.-L. (1998b) The role of formalism in the teaching of the theory of vector spaces, Linear Algebra and its Applications (275), 1(4), 1998, 141-160. Dorier J.-L. (1998c) On the teaching of the theory of vector spaces in first year of French science university, EduMath 6, 38-48. Dorier J.-L. (1995a) A General Outline of the Genesis of Vector Space Theory, Historia Mathematica 22(3), 227-261. Dorier J.-L. (1995b) Meta Level in the Teaching of Unifying and Generalizing Concepts in Mathematics, Educational Studies in Mathematics 29(2), 175-197. OUVRAGES COLLECTIFS Radford, L., Bartolini Bussi, M., Bekken, O., Boero, P., Dorier, J-L., Katz, V., Rodgers, L., Sierpinska, A. and Vasco, C. (2000) Historical formation and student understanding of mathematics (chapter 5), in Fauvel and van Maanen (eds), History in mathematics education - the ICMI-study, Dordrecht : Kluwer Academic Publisher, pp. 143-170.

75. History, Biographies, Classical Works - Virtual School Tasmania. 'hermann grassmann and the Creation of Linear Algebra' at. hermanngrassmann and the Prehistory of Universal Algebra' at. http http://www.en.eun.org/eun.org2/eun/en/vs-mathematics/content.cfm?lang=en&ov=5051

76. Histoire, Biographies, Oeuvres Classiques - Virtual School Translate this page hermann grassmann et la Création de l’Algèbre Linéaire’ sur le site. hermanngrassmann et la Préhistoire de l’Algèbre Universelle' sur le site. http://www.en.eun.org/eun.org2/eun/fr/vs-mathematics/content.cfm?lang=fr&ov=5051

77. Mathematica Information Center: Application Of Grassmann Algebra To Geometry Usi , From the Introduction hermann grassmann is an important figurein the historical development of the vector and tensor calculus....... http://library.wolfram.com/database/Articles/3418/

All Collections Articles Books Conference Proceedings Courseware Demos MathSource: Packages and Programs Technical Notes Title Application of Grassmann Algebra to Geometry Using Mathematica Authors G. Bitterfeld J. Browne J. Steiner Editors A. Easton J. Steiner Journal / Anthology The Role of Mathematics in Modern Engineering: Proceedings of AEMC '94 Year: Page range: Contents Introduction; Grassmann Approach to Geometry; The Mechanism Class; Mechanism Examples; Mechanism Synthesis; Conclusions Description From the Introduction: Hermann Grassmann is an important figure in the historical development of the vector and tensor calculus. In his book "Die Lineale Ausdehnungslehre" (Grassmann, 1862) Grassmann creates a mathematical language of significant power in its application to geometry. The word "Ausdehnungslehre" (exterior theory) is indicative of the fact that an element may be "extended" by taking the (exterior) product of it with another. For example, two distinct points may be "extended" into an element defining the straight line joining them by forming their exterior product. This element may be extended into an element defining a plane by multiplying it by a third point exterior to the line, and so on for higher dimensions. The "exteriorness" here is the geometric equivalent of "liner independence". If two elements are not exterior to one another (not independent) then their exterior product is zero. Grassmann, in the preface to his "Ausdehnungslehre" of 1862 said: "I am aware that the form which I have given the science is imperfect...there will come a time when these ideas, perhaps in a new form, will arise anew and will enter into living communication with contemporary developments" (Grassmann, 1862).

78. Mathematicians From DSB Translate this page Girard, Albert, 1595-1632. Göpel, Adolph, 1812-1847. grassmann, hermann Günther,1809-1877. Gregory, James, 1638-1675. Gua de Malves, Jean Paul de, $\sim$1712-1786. http://www.henrikkragh.dk/hom/dsb.htm

Last modification: document.write(document.lastModified) Webmaster Validate html Mathematicians from the Dictionary of Scientific Biography (DSB) Abel, Niels Henrik Argand, Jean Robert Artin, Emil Beltrami, Eugenio Berkeley, George Bertrand, Joseph Louis François Bianchi, Luigi Bolyai, János (Johann) Bolyai, Farkas (Wolfgang) Bolzano, Bernard Bombelli, Rafael Borel, Émile (Félix-Édouard-Justin) Bouquet, Jean-Claude Briot, Charles Auguste Cantor, Georg Carathéodory, Constantin Cardano, Girolamo Cauchy, Augustin-Louis Cayley, Arthur Chebyshev, Pafnuty Lvovich Clairaut, Alexis-Claude Clausen, Thomas Clebsch, Rudolf Friedrich Alfred Colden, Cadwallader Collinson, Peter Condorcet, Marie-Jean-Antoine-Nicolas Caritat, marquis de Cramer, Gabriel Crelle, August Leopold d'Alembert, Jean le Rond de Morgan, Augustus Dedekind, (Julius Wilhelm) Richard Delambre, Jean-Baptiste Joseph Descartes, René du Perron Dini, Ulisse Dirichlet, Gustav Peter Lejeune du Bois-Reymond, Paul David Gustav Duhamel, Jean Marie Constant Eisenstein, Ferdinand Gotthold Max Euclid

79. Helmholtz colors. It remained to hermann grassmann to prove a general resultin color opponency. Steven M. Boker Sun Feb 12 192436 EST 1995. http://kiptron.psyc.virginia.edu/steve_boker/ColorVision2/node7.html

80. Historia Matematica Mailing List Archive: Re: [HM] Caratheodory Dear John, Thank you very much for your reply. Concerning hermann G\ unther grassmann,it could be of special interest to have a look at hermann grassmann. http://sunsite.utk.edu/math_archives/.http/hypermail/historia/mar00/0116.html

Subject: From: Dominique Flament ( flament@msh-paris.fr Date: Tue Mar 21 2000 - 03:00:18 EST Next message: John McCleary: "Re: [HM] Olbers' paradox" Previous message: Abe Shenitzer: "[HM] Opinions on Grassmann's "Ausdehnungslehre"" In reply to: Reply: Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] [Bill Everdell] > 1844. So, it had occurred to me that, given the book's "geometrization" [John Conway] Dear John, Thank you very much for your reply. have a look at : Dimension et Puissance Selon l'Ausdehnung de Grassmann", Flament, Preface de D. Flament), Librairie Scientifique et Technique Albert Blanchard, Paris, 1994. vecteurs. Editions de la Maison des Sciences de l'Homme, Paris, 1997. by Lloyd. C. Kannenberg ; Forword by Albert C. Lewis). Open Court, Chicago and La Salle, Ilinois, 1995. (BSPS), Volume 187, Kluwer Academic Publishers, Dordrecht/Boston/London,1996. Arno Zaddach, Grassmanns Algebra in der Geometrie, mit Seitenblicken auf BI-Wissenschaftsverlag, 1994. * Flament Dominique * * F2DS (Bureau 308) * * Maison des Sciences de L'Homme * * 54, bd. Raspail, 75270 Paris Paris cedex 06 *

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