Hermann Grassmann

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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Grassmann, Hermann


Born Apr. 15, 1809, in Stettin; died there Sept. 26, 1877. German mathematician. Also worked in physics and philology.

Grassmann’s work The Calculus of Extension (1844) gave the first systematic construction of the study of n-dimensional Euclidean space and led to the development of vector analysis and tensor calculus. However, because of the abstract exposition and unusual terminology, the work was difficult to understand. In A Textbook of Arithmetic, Grass-mann attempted a strict exposition of the arithmetic of integers and in the process explained the role of definition by induction. In physics, he wrote on acoustics and the magnetic interaction of currents. Grassmann’s general ideas about abstract vector spaces led him to the discovery of an important idea—the possibility of studying color sensations as three-dimensional vectors, which is the basis for the modern study of color. He established the laws (1853) of color mixing. Grassmann also compiled a comprehensive dictionary of the hymns of Rig Veda (a monument of ancient Indian literature).


Gesammelte mathematische und physikalische Werke, vols. 1–3. Leipzig, 1894–1911.


Klein. F. Lektsii o razvitii matematiki ν 19 stoletii, part I. Moscow-Leningrad, 1937. (Translated from German.) [7–755-l]
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
In 1844, Hermann Gunter Grassmann published his book Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik [4], in which he developed the idea of an algebra in which the symbols representing geometric entities such as points, lines, and planes are manipulated using certain rules.
Kannenberg, A New Branch of Mathematics: The Ausdehnungslehre" of 1844 and Other Works, Open Court Publishing, Chicago, 1995.
Grassmann HG (1995) A new branch of mathematics: the Ausdehnungslehre of 1844 and other works.
Grassmann (1877), "Der Oft der Hamilton'schen Quaternionen in der Ausdehnungslehre", Mathematische Annalen, vol.
Grassmann's 1844 Ausdehnungslehre and Schleiermacher's Dialektik', Annals of Science, 34(2) (1977): 103-162 and Albert C.
Grassmann's 1844 Ausdehnungslehre and Schleiermacher's Dialektik", Annals of Science, 34(2) (1977): 103-162.
Grassmann (1877), "Der Ort der Hamilton'schen Quaternionen in der Ausdehnungslehre", Mathematische Annalen, vol.