1. 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.

2. WIEM: Grassmann Hermann Gunther grassmann hermann Günther (18091877), matematyk, fizyk i jezykoznawca niemiecki.Nauczyciel gimnazjalny w Szczecinie. Wspóltwórca rachunku http://wiem.onet.pl/wiem/01067d.html

WIEM 2004 - zobacz now± edycjê encyklopedii! Kup abonament i encyklopediê na CD-ROM, sprawd¼ ofertê cenow±! Oferta specjalna abonamentów dla szkó³ i instytucji! Uwaga! Przedstawione poni¿ej has³o pochodzi z archiwalnej edycji WIEM 2001! Prace redakcyjne nad edycj± 2001 zosta³y zakoñczone. Zapraszamy do korzystania z nowej, codziennie aktualizowanej i wzbogacanej w nowe tre¶ci edycji WIEM 2004 Matematyka, Fizyka, Jêzykoznawstwo, Niemcy Grassmann Hermann Gunther 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

3. Hermann Günther Grassmann --  Encyclopædia Britannica Grassmann, Hermann Günther Encyclopædia Britannica Article. Hermann Günther Grassmann. MLAstyle Hermann Gunther Grassmann. Encyclopædia Britannica. 2004. http://www.britannica.com/eb/article?eu=38531&tocid=0&query=hermann gunther gras

4. Hermann Grassmann 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.fact-index.com/h/he/hermann_grassmann.html

Main Page See live article Alphabetical index Hermann Grassmann ), was a mathematician physicist linguist , scholar, and 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 Justus Günther Grassmann 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. During that time his interest in mathematics arose and he wrote a treatise on the theory of the tides ( Theorie der Ebbe und Flut, His Geometrische Analyse Gottfried Wilhelm Leibniz . The award was given on July 1 The main mathematical works of Grassmann is found in his two books on the theory of extensive magnitudes ( Die lineale Ausdehnunglehre, ein neuer Zweig der Mathematik

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

espaces vectoriels abstraits La science des grandeurs extensives ou la théorie de l'espace (complété Hamilton introduisait le concept moderne de vecteur Vecteurs du plan (exposé élémentaire) d' 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; l'important , qui porte son nom : dimE + dimF = dim(E + F) + dim(E F) théorème homonyme concernant les applications linéaires Peano scalaires En savoir plus sur le produit scalaire le produit vectoriel La notation surlignée fléchée d'un vecteur , comme grasses éventuellement en italique : AB Stevin la notation des vecteurs Listing Liouville

6. Hermann Grassmann - Encyclopedia Article About Hermann Grassmann. Free Access, N encyclopedia article about Hermann Grassmann. Hermann Grassmann in Free onlineEnglish dictionary, thesaurus and encyclopedia. Hermann Grassmann. http://encyclopedia.thefreedictionary.com/Hermann Grassmann

Dictionaries: General Computing Medical Legal Encyclopedia Hermann Grassmann Word: Word Starts with Ends with Definition April 15 April 15 is the 105th day of the year in the Gregorian calendar (106th in leap years). There are 260 days remaining. Events 1450 - Battle of Formigny; Toward the end of the Hundred Years' War, the French attack and nearly annihilate English forces, ending English domination in northern France. 1632 - Battle of Rain; Swedes under Gustavus Adolphus defeat the Holy Roman Empire during the Thirty Years' War. Click the link for more information. Centuries: 18th century - 19th century - 20th century Decades: 1750s 1760s 1770s 1780s 1790s - Years: 1804 1805 1806 1807 1808 - Events First running of the Two Thousand Guineas Stakes horse race in England. January 16 - Peninsular War: The British defeat the French at the Battle of Corunna. Click the link for more information. September 26 September 26 is the 269th day of the year (270th in leap years) in the Gregorian Calendar, with 96 days remaining. Events 1580 - Sir Francis Drake circumnavigates the globe 1687 - The Parthenon in Athens is partially destroyed after an explosion caused by the bombing from Venetian forces led by Morozini who were besieging the Ottoman Turks stationed in Athens.

7. Hermann Günther Grassmann - Encyclopedia Article About Hermann Günther Grassma encyclopedia article about Hermann Günther Grassmann. Hermann Günther Grassmannin Free online English dictionary, thesaurus and encyclopedia. http://encyclopedia.thefreedictionary.com/Hermann Günther Grassmann

Dictionaries: General Computing Medical Legal Encyclopedia Hermann Günther Grassmann Word: Word Starts with Ends with Definition April 15 April 15 is the 105th day of the year in the Gregorian calendar (106th in leap years). There are 260 days remaining. Events 1450 - Battle of Formigny; Toward the end of the Hundred Years' War, the French attack and nearly annihilate English forces, ending English domination in northern France. 1632 - Battle of Rain; Swedes under Gustavus Adolphus defeat the Holy Roman Empire during the Thirty Years' War. Click the link for more information. Centuries: 18th century - 19th century - 20th century Decades: 1750s 1760s 1770s 1780s 1790s - Years: 1804 1805 1806 1807 1808 - Events First running of the Two Thousand Guineas Stakes horse race in England. January 16 - Peninsular War: The British defeat the French at the Battle of Corunna. Click the link for more information. September 26 September 26 is the 269th day of the year (270th in leap years) in the Gregorian Calendar, with 96 days remaining. Events 1580 - Sir Francis Drake circumnavigates the globe 1687 - The Parthenon in Athens is partially destroyed after an explosion caused by the bombing from Venetian forces led by Morozini who were besieging the Ottoman Turks stationed in Athens.

8. 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

9. Hermann Grassmann Hermann Grassmann. Hermann Günther Grassmann (1809 1877), byl matematik, fyzik,lingvista, ucenec, a neohumanist. Hermann Grassmann se narodil 15. http://wikipedia.infostar.cz/h/he/hermann_grassmann.html

švodn­ str¡nka Tato str¡nka v origin¡le Hermann Grassmann Hermann G¼nther Grassmann ), byl matematik fyzik lingvista , učenec, a neohumanist. Hermann Grassmann se narodil 15. dubna 1809 v Stettin (n¡hodou narozeniny Leonhard Euler ) a umřel 26. z¡Å™­ 1877 v Stettin. Jeho otec byl Justus G � nther Grassmann a jeho matka byla Johanne Luise Friederike Grassmann (d­vč­ jm©no: Medenwald). Hermann Grassmann byl syn učitele Å¡koly Justus Grassmann, Gymnasial - Profesor, kdo psal několik vlivn½ch knih o fyzice a matematice a různ© pozn¡mky ( Schulprogramme ) kter½ zapůsobil na jeho syna Hermann. Shodovat se k biografick© studii H. Grassmann s¡m, on byl pomal½ v institute a jeho otec zaměřil jej k kari©Å™e jako zahradn­k. Nicm©ně, on dokončil tělocvičnu s vysokou zn¡mkou a pokračoval k Berl­n spolu s jeho bratrem studovat na pan¡Äka. Během toho měřit jeho z¡jem v matematika vyvst¡val a on napsal pojedn¡n­ na teorii př­livů ( Theorie der Ebbe und Flut, Pr¼fungsarbeit 1840, publikoval Justus Grassmann) ke stupni pro matematickou učitelskou pozici. Jeho Geometrische analyzovat byl poddal se F¼rstliche Jablonowski'schen Gesellschaft, jak jedin½ kandid¡t, obnovit nebo k nově vynal©zt osu-voln½ geometrick½ počet v duchu

10. Hermann Grassmann - Information An online Encyclopedia with information and facts Hermann Grassmann Information,and a wide range of other subjects. Hermann Grassmann - Information. http://www.book-spot.co.uk/index.php/Hermann_Grassmann

Hermann Grassmann - Information Home Mathematical and natural sciences Applied arts and sciences Social sciences and philosophy ... Interdisciplinary categories ), was a mathematician physicist linguist , scholar, and 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 Justus Günther Grassmann 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. During that time his interest in mathematics arose and he wrote a treatise on the theory of the tides ( Theorie der Ebbe und Flut

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. Geometric Calculator - Glossary American mathematical physicist. 18391903. Grade grassmann hermann Grassmann.German scholar. 1809-1877. Hamilton Sir William Rowan Hamilton. http://www.elf.org/calculator/gloss.html

Start Calculator Home Introduction Reference Glossary Bugs Bibliography Links Geometric Calculator - Glossary Here are some terms and people who deserve definitions. 0-vector A scalar 1-vector A vector 2-vector A bivector 3-vector A trivector Bivector Blade Hestenes' term for a multivector with no scalar part, to emphasise their directional nature. Clifford William Kingdon Clifford. English geometer. 1845-1879. "If he had lived we might have known something." Complex number Conjugation Dilation To change in magnitude or scale, as by multiplying by a scalar. Also written as dilatation. Flat A linear subspace. Floating point number A computer approximation to a real number Geometric product Gibbs Josiah Willard Gibbs. American mathematical physicist. 1839-1903. Grade Grassmann Hermann Grassmann. German scholar. 1809-1877. Hamilton Sir William Rowan Hamilton. Irish mathematical physicist. 1805-1865. Heavisides Oliver Heavisides. English researcher. 1850-1925. Hestenes David Hestenes.

13. Hermann Grassmann 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.sciencedaily.com/encyclopedia/hermann_grassmann

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14. 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.

15. Introduction To Translation Of Grassmann's Ausdehnungslehre Introduction. hermann grassmann s 1862 Ausdehnungslehre (literally, ``Theory ofExtension ) is one of the great mathematical works of the nineteenth century. 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

16. Grassmann, Hermann Gunther. The Columbia Encyclopedia, Sixth Edition. 2001 The Columbia Encyclopedia, Sixth Edition. 2001. grassmann, hermann Günther. http://www.bartleby.com/65/gr/Grassman.html

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17. Grassmann, Hermann Günther Search Biographies Bio search tips grassmann, hermann Günther Pronunciation Key. grassmann, hermann Günther , 180977, German mathematician and Sanskrit scholar, educated in http://www.infoplease.com/cgi-bin/id/A0821587.hmtl

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18. Grassmann Biography of hermann grassmann (18091877) hermann Günter grassmann. Born 15 April 1809 in Stettin, Prussia (now Szczecin, Poland) hermann grassmann is chiefly remembered for his development 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.

19. Hermann Günther Grassmann --  Encyclopædia Britannica MLA style " hermann Gunther grassmann." Encyclopædia Britannica. 2004 APA style hermann Gunther grassmann. Encyclopædia Britannica. Retrieved April 2, 2004, from Encyclopædia http://www.britannica.com/eb/article?eu=38531

20. Hankel of formal laws, he developed complex numbers as well as such higher algebraic systemsas Möbius barycentric calculus, some of hermann grassmann s algebras http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Hankel.html

Hermann Hankel Born: 14 Feb 1839 in Halle, Germany Died: Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Hermann Hankel 's father was Wilhelm Gottlieb Hankel who was a physicist at Halle at the time Hermann was born. Hermann began his education in Halle but, in 1849 Wilhelm was appointed to the chair of physics at Leipzig so the family moved to Leipzig where Hermann attended the Nicolai Gymnasium. At the gymnasium he [1]:- ... improved his Greek by reading the ancient mathematicians in the original. In 1857 Hankel entered the University of Leipzig where he studied mathematics with Riemann and then, in the following year, he worked with Weierstrass and Kronecker in Berlin. He received his doctorate for a thesis in 1862. Hankel's habilitation He worked on the theory of complex numbers, the theory of functions and the history of mathematics. His work on complex analysis, however, is not considered of the first rank and in [8] he is included with those who contributed but whose:- ... influence on the foundations of complex analysis was not as essential as that of those mathematicians discussed in more detail Riemann Weierstrass Hurwitz Bieberbach Hankel made a systematic study of the rules of arithmetic with his Prinzip der Permanenz der formalen Gesetze (1867), see [7]. He wrote another important work which was also published in 1867

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