1. Hermann Günther Grassmann - Encyclopedia Article From Britannica.com Search Hermann Günther Grassmann at Britannica.com for the Web's best sites, news and magazine articles, and related http://www.britannica.com/seo/h/hermann-gunther-grassmann

Search at Britannica.com for the Web's best sites, news and magazine articles, and related products. To view the complete article, sign up for Britannica's premium service - Grassmann, Hermann Gnther b. April 15, 1809, Stettin, Prussia [now Szczecin, Pol.] d. Sept. 26, 1877, Stettin, Ger. German mathematician chiefly remembered for his development of a general calculus of vectors in Die line ale Ausdehnungslehre, ein neuer Zweig der Mathematik (1844; "The Theory of Linear Extension, a New Branch of Mathematics"). Grassmann Need more? Complete articles are available to premium service members. Information on site licenses is also available. About Us Advertise With Us Syndication International Publishing ... Help

2. Grassmann Hermann Günter Grassmann. Born Hermann Grassmann is chiefly rememberedfor his development of a general calculus for vectors. Grassmann http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Grassmann.html

Born: 15 April 1809 in Stettin, Prussia (now Szczecin, Poland) Died: 26 Sept 1877 in Stettin, Germany (now Szczecin, Poland) Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index 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 Ausdehnungslehre, 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 invented what is now called Exterior Algebra. This was joined to Hamilton 's quaternions by Clifford in 1878. Clifford replaced Grassmann's rules e p e p = and e p e q e q e p for p q by the rules e p e p = 1 and e p e q e q e p for p q Clifford algebras are used today in the theory of quadratic forms and in relativistic quantum mechanics and they appear together with Grassmann's exterior algebra in differential geometry . See [26]. Grassmann's methods were slow to be adopted but eventually they inspired the work of Elie Cartan and have since been used in studying differential forms and their application to analysis and geometry.

3. WIEM: Grassmann Hermann Gunther (encyklopedia.pl)Category World Polska Leksykon Encyklopedia encyklopedia.pl G......grassmann hermann Günther (18091877), matematyk, fizyk i jezykoznawca niemiecki.Nauczyciel gimnazjalny w Szczecinie. Wspóltwórca rachunku http://wiem.onet.pl/wiem/01067d.html

wiem.onet.pl napisz do nas losuj: has³a multimedia Matematyka, Fizyka, Jêzykoznawstwo, Niemcy Grassmann Hermann Gunther widok strony znajd¼ podobne poka¿ powi±zane Grassmann Hermann Günther (1809-1877), matematyk, fizyk i jêzykoznawca niemiecki. Nauczyciel gimnazjalny w Szczecinie. Wspó³twórca rachunku wektorowego , autor prac z zakresu geometrii n-wymiarowej i algebry liniowej, akustyki optyki Twórca tzw. praw Grassmanna dotycz±cych mieszania barw: 1) ka¿da ci±g³a zmiana promieniowania wywo³uje ci±g³± zmianê barwy, 2) przy sk³adaniu dwóch promieniowañ barwa wypadkowa zale¿y tylko od barw sk³adowych, 3) ka¿d± barwê mo¿na utworzyæ z 3 liniowo niezale¿nych barw (np. czerwonej, zielonej i fioletowej). Od ok. 1862 podj±³ porównawcze studia nad sanskrytem - sformu³owa³ prawo dysymilacji spó³g³osek aspirowanych w grece i jêzyku staroindyjskim, bada³ s³ownictwo Rygwedy Niektóre prace: Die Wissenschaft der extensiven Grösse, oder die Ausdehnungslehre... Wörterbuch zum Rig-Veda zobacz wszystkie serwisy do góry Encyklopedia zosta³a opracowana na podstawie Popularnej Encyklopedii Powszechnej Wydawnictwa Fogra

4. WIEM: Rachunek Wektorowy Powiazania. grassmann hermann Gunther, Hamilton Sir William Rowan, wiecej». Copyright 19962001 Onet.pl SA - zobacz wszystkie serwisy », do góry. http://wiem.onet.pl/wiem/00d8c1.html

wiem.onet.pl napisz do nas losuj: has³a multimedia Matematyka Rachunek wektorowy widok strony znajd¼ podobne poka¿ powi±zane Rachunek wektorowy, dzia³ matematyki, czê¶æ geometrii analitycznej ( geometria ) rozwijany w XIX w. (g³ównie przez W.R. Hamiltona ), badaj±cy w³asno¶ci dzia³añ na wektorach Uogólnieniem rachunku wektorowego jest rachunek tensorowy ( tensor Powi±zania Grassmann Hermann Gunther Hamilton Sir William Rowan wiêcej zobacz wszystkie serwisy ... do góry Encyklopedia zosta³a opracowana na podstawie Popularnej Encyklopedii Powszechnej Wydawnictwa Fogra

5. Grassmann Translate this page grassmann hermann Günther allemand, 1809-1877 Professeur de mathématiquesà Stettin (alors ville prussienne, en Poméranie, sur http://www.sciences-en-ligne.com/momo/chronomath/chrono1/Grassmann.html

allemand, 1809-1877 espaces vectoriels abstraits La science des grandeurs extensives ou la théorie de l'espace (complété Hamilton introduisait le concept moderne de vecteur de somme de sous-espaces; de , correspondant au produit scalaire actuel : de produit , qui deviendra, en dimension 3, avec Gibbs et Clifford , notre produit vectoriel usuel; dimE + dimF = dim(E + F) + dim(E F) Peano scalaires produit scalaire produit vectoriel grasses éventuellement en italique : AB Stevin la notation des vecteurs Listing Liouville

6. Hermann Grassmann Hermann Grassmann Papers by Desmond FearnleySander. Desmond Fearnley-Sanderhas made available on the Web a number of papers relating http://www.maths.tcd.ie/pub/HistMath/People/Grassmann/dfs.html

Hermann Grassmann: Papers by Desmond Fearnley-Sander Desmond Fearnley-Sander has made available on the Web a number of papers relating to Hermann Grassmann (1809-1877). These include: Hermann Grassmann and the Creation of Linear Algebra Hermann Grassmann and the Prehistory of Universal Algebra Grassmann's Theory of Dimension

7. Hermann Grassmann - Wikipedia Hermann Grassmann. Hermann Grassmann was born on April 15, 1809 in Stettin (by chancethe birthday of Leonhard Euler) and died on September 26, 1877 in Stettin. http://www.wikipedia.org/wiki/Hermann_Grassmann

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles Interlanguage links All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Hermann Grassmann From Wikipedia, the free encyclopedia. mathematician physicist linguist , scholar, neohumanist Hermann Grassmann was born on April 15, 1809 in Stettin (by chance the birthday of Leonhard Euler ) and died on September 26, 1877 in Stettin. His father was and his mother was Johanne Luise Friederike Grassmann (maiden name: Medenwald). Hermann Grassmann was the son of the school teacher Justus Grassmann, Gymnasial -Professor, who wrote several influential books on physics and mathematics and various notes ( Schulprogramme ) which influenced his son Hermann. According to a biographical sketch by H. Grassmann himself, he was slow in school, and his father pointed him to an career as gardener. However, he finished the Gymnasium with a high grade and went on to Berlin together with his brother studying theology.

8. Hermann Grassmann Hermann Grassmann. Hermann Grassmann on equality further relations of equalityemerge. . Hermann Grassmann and the Creation of Linear Algebra. Ahmet Gorgun. http://home.att.net/~agorgun/Grsmn.htm

Home On Space On Isaac Newton Knowledge = Ratio Hermann Grassmann Hermann Grassmann on equality "Since two equals must appear as different in order to stand out as two, and two differents must appear as different aspects of equals, it seems necessary from a superficial consideration to formulate various relations of equality and difference. Thus for example in comparing two line segments one can assert equality of direction or length, of direction and length, of direction and position, and so forth; and in comparing other things, further relations of equality emerge." Hermann Grassmann and the Creation of Linear Algebra Ahmet Gorgun February 2002

9. Advanced Search View Basket Your Account Order Status Help Home Your search for grassmann+hermann yielded 3 results using author Displayingresults 1 to 3. 1. Worterbuch zum Rigveda - Grassmann http://www.countrybookshop.co.uk/cgi-bin/search.pl?searchtype=author&searchtext=

10. Hermann Gunter Grassmann - Acapedia - Free Knowledge, For All Friends of Acapedia Hermann Gunter Grassmann. From Wikipedia, the free encyclopedia.(There is currently no text in this page). Current Events. Sciences. http://acapedia.org/aca/Hermann_Gunter_Grassmann

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11. Grassmann Hermann Grassmann (along with William Rowan Hamilton) invented vector and tensoralgebra in 1844, but was unable to attract attention to the new method http://kiptron.psyc.virginia.edu/steve_boker/ColorVision2/node8.html

12. Grassmanians The origin of the word Grassmannian comes from the name of a mathematician grassmann hermann Günther (1809-1877). He was also a physicist. http://math.uwb.edu.pl/~mariusz/html/grassmanians.html

A Primer on Grassmannians Preface. Writing this text, the only wish I had, was to give an introductory account on some geometries I am concerned about. As for prerequisites, the reader is expected to be familiar with basics of linear algebra. I have tried to make this text clear for a wide range of visitors, so it may occur trivial for experienced readers. The origin of the word G rassmannian comes from the name of a mathematician - Grassmann Hermann G nther (1809-1877). He was also a physicist. He formulated Three Rules of Colour Blending. One of them says that each colour can be obtained by blending 3 linearly independent colours e.g. red, green, violet. He gave foundations for vector and tensor calculus. His vector-like approach to the geometry of n -dimensional spaces led to axiomatic definition of linear spaces. He gave basic rules for natural numbers (before Peano) and created arithmetic of negative numbers. The term G rassmannian refers to a variety of structures built in vector spaces. It is used in topological geometry, differential geometry and phisics. All of those Ggrassmannians have one common feature. Namely, the universe is the same in all cases. In a fixed vector space V , one can distinguish subspaces of a given dimension, say k . They form a set, denoted by Sub

13. Introduction To Translation Of Grassmann's Ausdehnungslehre Explains the published paper called Ausdehnungslehre, which translates to Theory of Extension . The purpose is to create a universal type of geometric calculus. This development is used in linear and nonlinear algebra, today. http://www.maths.utas.edu.au/People/dfs/Papers/GrassmannTranslation/node3.html

NEXT PAGE CONTENTS PREVIOUS PAGE Introduction Hermann Grassmann's 1862 Ausdehnungslehre (literally, ``Theory of Extension'') is one of the great mathematical works of the nineteenth century. In it the foundations of linear and multilinear algebra are laid and much of the superstructure too is constructed. It is regrettable that such a book on such a subject should, from the moment of publication, have been not much read. Indeed, Grassmann's reputation for impenetrability has persisted to this day. Yet one may suspect that a writer who is, in many respects, a century ahead of his time will be somewhat more readable when that century has elapsed than he was to his contemporaries. It is my hope that this translation and commentary will make it easy for today's mathematically educated reader to appreciate Grassmann's presentation of the theory of basis and dimension - it does not differ much from the initial chapter of a modern linear algebra text. The work called simply Die Ausdehnungslehre , though its title page bears the date 1862, actually appeared in the latter half of 1861. It was Grassmann's second attempt to present his theory and was totally different in conception from

14. Grassmann Algebra A page on grassmann, grassmann algebra, and the book I am writing on grassmann algebra in Mathematica. science is his collected works grassmann, hermann. hermann grassmanns Gesammelte Mathematische und Physikalische Werke. http://www.ses.swin.edu.au/homes/browne/grassmannalgebra

Grassmann Algebra Site map John Browne's Home Page Grassmann Algebra Book Programming for Engineers Course Notes Probabilistic Design ... Course Notes Index to this page Grassmann Algebra Hermann Grassmann Grassmann Algebra Book Mathematica ... Contact Details Grassmann Algebra What is Grassmann Algebra? Grassmann algebra is a mathematical system which predates vector algebra, and yet is more powerful than it, subsuming and unifying much of the algebra used by engineers and physicists. It has remained relatively unknown since its discovery over 160 years ago, yet is now emerging as a potential mathematical system for describing such diverse applications as robotic manipulators and fundamental physical theories. Where does its power come from? The intrinsic power of Grassmann algebra arises from its fundamental product operation, the exterior product. The exterior product codifies the property of linear dependence directly into the algebra. Simple non-zero elements of the algebra are products of linearly independent elements. For example, a simple bivector is the exterior product of two independent vectors; a line is represented by the exterior product of two independent points and a plane is represented by the exterior product of three independent points. The best original source to Grassmann's contributions to mathematics and science is his collected works: Grassmann, Hermann

15. Grassmann Biography of hermann grassmann (18091877) hermann Günter grassmann. Born 15 April 1809 in Stettin, Prussia (now Szczecin, Poland) http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Grassmann.html

Born: 15 April 1809 in Stettin, Prussia (now Szczecin, Poland) Died: 26 Sept 1877 in Stettin, Germany (now Szczecin, Poland) Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index 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 Ausdehnungslehre, 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 invented what is now called Exterior Algebra. This was joined to Hamilton 's quaternions by Clifford in 1878. Clifford replaced Grassmann's rules e p e p = and e p e q e q e p for p q by the rules e p e p = 1 and e p e q e q e p for p q Clifford algebras are used today in the theory of quadratic forms and in relativistic quantum mechanics and they appear together with Grassmann's exterior algebra in differential geometry . See [26]. Grassmann's methods were slow to be adopted but eventually they inspired the work of Elie Cartan and have since been used in studying differential forms and their application to analysis and geometry.

16. References For Grassmann References for hermann grassmann. D FearnleySander, hermann grassmann and thecreation of linear algebra, Amer. Math. Monthly 86 (10) (1979), 809-817. http://www-gap.dcs.st-and.ac.uk/~history/References/Grassmann.html

References for Hermann Grassmann Biography in Dictionary of Scientific Biography (New York 1970-1990). Biography in Encyclopaedia Britannica. Articles: A Beutelspacher, A survey of Grassmann's 'Lineale Ausdehnungslehre', in (Dordrecht, 1996), 3-6. A Brigaglia, The influence of H Grassmann on Italian projective n-dimensional geometry, in (Dordrecht, 1996), 155-163. A Brini and A G B Teolis, Grassmann progressive and regressive products and CG-algebras, in (Dordrecht, 1996), 231-242. 1830-1930 : a century of geometry (Berlin, 1992), 222-244. Linear and Multilinear Algebra Hermann Grassmann (Greifswald, 1995), 33-36. D Fearnley-Sander, Hermann Grassmann and the creation of linear algebra, Amer. Math. Monthly D Fearnley-Sander, Hermann Grassmann and the prehistory of universal algebra, Amer. Math. Monthly D Fearnley-Sander, Grassmann's theory of dimension, in First Australian Conference on the History of Mathematics (Clayton, 1981), 52-82. 1830-1930 : a century of geometry (Berlin, 1992), 205-221. N A Gordienko, The concept of 'fraction' in H Grassmann's 'Die Ausdehnungslehre' and its connection with contemporary linear algebra (Russian)

17. Hermann Grassmann And The Prehistory Of Universal Algebra hermann grassmann and the Prehistory of Universal Algebra This paper appeared in the American Mathematical Monthly 89 (1982), 161166. Your comments are welcome dfs@hilbert.maths.utas.edu.au http://www.maths.utas.edu.au/People/dfs/Papers/GrassmannUAlgpaper/GrassmannUAlgp

NEXT PAGE Hermann Grassmann and the Prehistory of Universal Algebra Desmond Fearnley-Sander Universal Algebra A Sketch of the Prehistory of Universal Algebra Grassmann and Boole ... References This paper appeared in the American Mathematical Monthly 89 (1982), 161-166. Your comments are welcome: dfs@hilbert.maths.utas.edu.au This html document was generated using the LaTeX HTML Nikos Drakos , Computer Based Learning Unit, University of Leeds. Links Go Key Resource History of Mathematics

18. Hermann Grassmann And The Creation Of Linear Algebra NEXT PAGE. hermann grassmann and the Creationof Linear Algebra. Desmond FearnleySander. http://www.maths.utas.edu.au/People/dfs/Papers/GrassmannLinAlgpaper/GrassmannLin

NEXT PAGE Hermann Grassmann and the Creation of Linear Algebra Desmond Fearnley-Sander Introduction Grassmann's life The invention of linear algebra ... References This paper appeared in the American Mathematical Monthly 86 (1979), 809-817. Your comments are welcome: dfs@hilbert.maths.utas.edu.au This html document was generated using the LaTeX HTML Nikos Drakos , Computer Based Learning Unit, University of Leeds.

19. Grassmann, Hermann Gunther. The Columbia Encyclopedia, Sixth Edition. 2001 grassmann, hermann Günther. (h r´män gün´t r gräs´män) (KEY) , 180977, German mathematician and Sanskrit http://www.bartelby.com/65/gr/Grassman.html

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20. Grassmann, Hermann Gunther. The Columbia Encyclopedia, Sixth Edition. 2001 2001. grassmann, hermann Günther. (h r´män gün´t r gräs´män) (KEY) ,1809–77, German mathematician and Sanskrit scholar, educated in Berlin. http://www.bartleby.com/65/gr/Grassman.html

Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Reference Columbia Encyclopedia PREVIOUS NEXT ... BIBLIOGRAPHIC RECORD The Columbia Encyclopedia, Sixth Edition. (h KEY Die Ausdehnungslehre CONTENTS INDEX GUIDE BIBLIOGRAPHIC RECORD ... NEXT Search Amazon: Click here to shop the Bartleby Bookstore Welcome Press Advertising ... Bartleby.com

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