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	Hermann Grassmann Summary
		Hermann Grassmann was the third of 12 children of Justus Günter Grassmann, an ordained minister who taught mathematics and physics at the Stettin Gymnasium, where Hermann was educated.
		A son, Hermann Ernst Grassmann, became a professor of mathematics at the University of Giessen.
		Grassmann then showed that once geometry is put into the algebraic form he advocated, then the number three has no privileged role as the number of spatial dimensions; the number of possible dimensions is in fact unbounded.
	www.bookrags.com /Hermann_Grassmann (2736 words)

	Hermann Grassmann - Wikipedia, the free encyclopedia
		Hermann Günther Grassmann (April 15, 1809 – September 26, 1877) was a German mathematician, physicist, linguist, scholar, and neohumanist.
		Grassmann was born in Stettin (by chance, on the birthday of Leonhard Euler) and died there in 1877.
		Grassmann is best known to linguists for his work on an important sound law of Indo-European, today called Grassmann's Law in his honor.
	en.wikipedia.org /wiki/Hermann_Grassmann (614 words)

	Grassmann biography
		Hermann Grassmann's father was Justus Günter Grassmann and his mother was Johanne Luise Friederike Medenwald, who was the daughter of a minister from Klein-Schönfeld.
		Grassmann felt somewhat aggrieved that he was producing highly innovative mathematics which he felt was important yet he was still teaching in secondary schools.
		Grassmann's mathematical 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.
	www-history.mcs.st-and.ac.uk /history/Biographies/Grassmann.html (2579 words)

	Encyclopedia: Hermann Grassmann
		In mathematics, the exterior algebra (also known as the Grassmann algebra) of a given vector space V is a certain unital associative algebra which contains V as a subspace.
		Grassmanns Law is a rule of phonology in Ancient Greek and Sanskrit which states that if an aspirated consonant is followed by an aspirated consonant in the next syllable, the first one loses the aspiration.
		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.
	www.nationmaster.com /encyclopedia/Hermann-Grassmann (1580 words)

	Hermann Grassmann - Encyclopedia, History, Geography and Biography (Site not responding. Last check: 2007-11-02)
		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 a career as gardener.However, he finished the Gymnasium with a high grade and went on to Berlintogether with his brother studying theology.
		Hermann Grassmann, Works on mathematics, Theory of extensive magnitudes, Works on linguistics, Children, References, External links, 1809 births, 1877 deaths, 19th century mathematicians, German linguists, German mathematicians and German physicists.
	www.arikah.net /encyclopedia/Grassmann (650 words)

	Hermann Grassmann: Definition and Links by Encyclopedian.com - All about Hermann Grassmann (Site not responding. Last check: 2007-11-02)
		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.
		Grassmann was awarded the title of Gymnasial-Professor and had to stay as school treacher in Stettin.
		The space of a Grassmann algebra can hence be decomposed into a direct sum of homogenous subspaces of definite grade, i.e.
	www.encyclopedian.com /he/Hermann-Grassmann.html (794 words)

	Hermann Grassmann (Site not responding. Last check: 2007-11-02)
		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.
		Grassmann was not only a great mathematician, he was doing research in physics, (crystallography, electromagnetism, mechanics, etc), physiology (theory of colours,theory of vocals).
		Grassmann is best known to linguists for his work on an important sound law of Indo-European, today called Grassmann'sLaw in his honor.
	www.therfcc.org /hermann-grassmann-181716.html (549 words)

	Hermann Grassmann - Wikipedia, la enciclopedia libre
		Hermann apreciaba la música y aprendió a tocar el piano, a la vez que proseguía sus estudios, en los que poco a poco iba mejorando y en los exámenes finales de los estudios secundarios, con 18 años, terminó el segundo de su promoción.
		Grassmann demostró además que si la geometría se hubiese expresado en forma algebraica como él proponía, el número tres no hubiese desempeñado el papel privilegiado que tiene como número que expresa la dimesiones espaciales; de hecho, el número de posibles dimensiones de interés para la geometría es ilimitado.
		Grassmann escribió también sobre cristalografía, electromagnetismo, y mecánica.
	es.wikipedia.org /wiki/Hermann_Grassmann#Biograf.C3.ADa (2125 words)

	Grassmann's law - Wikipedia, the free encyclopedia
		For Grassmann's law in color theory, see CIE 1931 color space.
		Grassmann's law, named after its discoverer Hermann Grassmann, is a rule of phonology in Ancient Greek and Sanskrit which states that if an aspirated consonant is followed by an aspirated consonant in the next syllable, the first one loses the aspiration.
		In the reduplication which forms the perfect tense in both Greek and Sanskrit, if the initial consonant is aspirated, the prepended consonant is unaspirated by Grassmann's Law.
	en.wikipedia.org /wiki/Grassmann's_law (356 words)

	Read about Hermann Grassmann at WorldVillage Encyclopedia. Research Hermann Grassmann and learn about Hermann Grassmann ... (Site not responding. Last check: 2007-11-02)
		Hermann Grassmann was born in Stettin (by chance, on the birthday of
		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,
	encyclopedia.worldvillage.com /s/b/Hermann_Grassmann (538 words)

	John Browne's Home Page
		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.
		Hermann Grassmann was a German schoolteacher who lived from 1809 to 1877.
	www.grassmannalgebra.info (428 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		Grassmann, more successfully than any other scholar of his age, pursued the vision of that ideal unity, and upon it he rested his seminal achievements.
		Justus Gnther Grassmann and Dynamist Naturphilosophie; M.-L. Heuser.
		The Influence of Hermann Gnther Grassmann and Robert Grassmann on Ernst Schrder's Algebra of Logic; V. Peckhaus.
	www.clifford.org /anonftp/pub/books/schubring.txt (498 words)

	Grassmann (Site not responding. Last check: 2007-11-02)
		Hermann Grassmann is chiefly remembered for his development of a general calculus for vectors.
		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.
		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.
	www.bg-rams.ac.at /intranet/Physik/history/Grassmann.html (230 words)

	Hermann Grassmann - RecipeFacts (Site not responding. Last check: 2007-11-02)
		Hermann Günther Grassmann (April 15, 1809 – September 26, 1877) was a German mathematician, physicist, linguist, scholar, and neohumanist.
		His son Hermann Ernst Grassmann (1857-1922), also called Hermann Grassmann der jungere (the younger), was also a mathematician.
		Hermann Grassmann and the Creation of Linear Algebra [3]hu:Hermann Günter Grassmann
	www.recipeland.com /encyclopaedia/index.php/Hermann_Grassmann (609 words)

	A History of Hypercomplex Numbers (Site not responding. Last check: 2007-11-02)
		Hermann Grassmann (1809-1877) begins work on his exterior algebra (through 1862), beginning with his work of this year, Science of Linear Extensions, dealing with the geometry of n-dimensional spaces.
		Grassmann publishes a 2nd edition of his Science of Linear Extensions, being more accessible and popular among mathematicians, elaborating on linear (in)depedence, subsets, intersections, and laying stress on the distinction between inner and outer products.
		Hermann Hankel (1839-1873) publishes Theory of complex numbers, containing a proof that complex numbers are the most general algebra that is possible under the fundamental laws of arithmetic, also helping to popularize Grassmann's ideas.
	history.hyperjeff.net /hypercomplex.html (2046 words)

	Evolution of Geometric Algebra and Calculus
		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 [1888] and Whitehead [1848], but their work failed to advance or promulgate his vision.
		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).
	modelingnts.la.asu.edu /html/evolution.html (745 words)

	Historia Matematica Mailing List Archive: Re: [HM] Caratheodory
		Grassmann", {\it Lectures Notes in Physics}, {\bf 402} (1992), {\it
		Gert Schubring (ed.), Hermann G\"unther Grassmann (1809-1877): Visionary
		Arno Zaddach, Grassmanns Algebra in der Geometrie, mit Seitenblicken auf
	sunsite.utk.edu /math_archives/.http/hypermail/historia/mar00/0116.html (408 words)

	Grassmann, Hermann Günther (Site not responding. Last check: 2007-11-02)
		Grassmann was born in Stettin, Pomerania (now Szczecin, Poland), and studied at Berlin.
		Grassmann developed his method of calculus, which he called the theory of extension, from 1840.
		Grassmann learned and examined many ancient languages, such as Persian, Sanskrit, and Lithuanian.
	www.cartage.org.lb /en/themes/Biographies/MainBiographies/G/Grassmann/1.html (140 words)

	[No title]
		Hermann Grassmann (1809-1877) became a Sanskrit scholar, but in his spare time turned to mathematical research because of his father's interests.
		The frequent duplication of Grassmann's discoveries is not a mark of limited originality but rather a sign that Grassmann was keenly attuned to a powerful thematic force driving mathematical development, namely, the subtle interplay between geometry and algebra.
		....Grassmann's idea was to develop a calculus for the join and meet of linear varieties in projective space, a calculus that is actually realized by the progressive [outer] and the regressive [inner] products....[T]he dual space V
	members.fortunecity.com /jonhays/grassmann.htm (585 words)

	Chapterten.html (Site not responding. Last check: 2007-11-02)
		Grassmann's is one of the celebrated articles of linguistics.
		Grassmann's achievement is great, even though he left a field for Verner to conquer.
		Hermann Grassmann (1809-1877) was a banker who was compelled to retire because of tuberculosis.
	www.utexas.edu /cola/depts/lrc/iedocctr/ie-docs/lehmann/reader/Chapter10.html (7553 words)

	Hermann Gunther Grassmann -- Encyclopædia Britannica
		German mathematician chiefly remembered for his development of a general calculus of vectors in Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik (1844; “The Theory of Linear Extension, a New Branch of Mathematics”;).
		It was German psychologist Hermann Ebbinghaus who demonstrated that scientific methods could be applied to the study and measurement of the mental processes involved in rote learning.
		Dramatist and novelist Hermann Sudermann was one of the leading writers of the German naturalist movement.
	www.britannica.com /eb/article-9037770?tocId=9037770 (475 words)

	About "Hermann Grassmann and the Prehistory of Universal Algebra" (Site not responding. Last check: 2007-11-02)
		Hermann Grassmann and the Prehistory of Universal Algebra
		A definition of universal algebra, with a sketch of its prehistory.
		Here the term 'family of algebras of a given species' is used in a technical sense meaning a class closed under taking subalgebras, homomorphic images and direct products - or what is nowadays called a variety.
	mathforum.org /library/view/3253.html (135 words)

	Application of Grassmann Algebra to Geometry Using Mathematica -- from Mathematica Information Center
		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.
		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).
	library.wolfram.com /infocenter/Articles/3418 (257 words)

	ScienceDaily: Hermann grassmann (Site not responding. Last check: 2007-11-02)
		Look for Hermann grassmann in Wiktionary, our sister dictionary project.
		Look for Hermann grassmann in the Commons, our repository for free images, music, sound, and video.
		Check for Hermann grassmann in the deletion log, or visit its deletion vote page if it exists.
	www.sciencedaily.com /encyclopedia/hermann_grassmann (892 words)

	Amanda.html (Site not responding. Last check: 2007-11-02)
		Hermann Grassmann is not credited much for inventing Linear Algebra, however, many believe that he was the inventer.
		Grassmann did not put much of his work in writing.
		One example that was in the American Matematically monthly was that he come up with the definition of a vector space.
	www.mathsci.appstate.edu /~sjg/class/2240/finalss04/Amanda.html (1088 words)

	Hermann Günther Grassmann - rFind.net (Site not responding. Last check: 2007-11-02)
		Grassmann skapade genom Ausdehnungslehre (1844) en ny gren av matematiken, i vilken
		geometri ingick som en särskild del. Grassmanns metoder består huvudsakligen i användningen av nya komplexa tal med flera enheter än den reella och imaginära.
		Hermann Paul StartsidaSenaste nyttLänkspegelInställningarHermann Paul, lingvist, född 1846, död 1921, Tyskland.
	www.rfind.net /info/Hermann_G%FCnther_Grassmann (228 words)

	AllRefer.com - Hermann GUnther Grassmann (Language And Linguistics, Biography) - Encyclopedia
		AllRefer.com - Hermann GUnther Grassmann (Language And Linguistics, Biography) - Encyclopedia
		Hermann GUnther Grassmann[her´mAn gUn´tur grAs´mAn] Pronunciation Key, 1809–77, German mathematician and Sanskrit scholar, educated in Berlin.
		More articles from AllRefer Reference on Hermann Gunther Grassmann
	reference.allrefer.com /encyclopedia/G/Grassman.html (198 words)

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