Hermann Grassmann(redirected from Ausdehnungslehre)
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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).