Reye, Theodor

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(b. Ritzebuttel, near Cuxhaven, Germany, 20 June 1838; d. Wurzburg, Germany, 2 July 1919)


After schooling in Humburg, Reye studied mechanical engineering and then mathematical physics at Hannover, Zurich, and Gōttingen. He received his doctorate at Gōttingen in 1861 with a disertation on gas dynamics. After qualifying as lecture at Zurich in 1863, he remained there until 1870 as a Privadozent in mathematical physics. Following a short stay in Aachen came his most productive years 1872–1909, when he was professor of geometry at the University of strasbourg. He remained in Strasbourg until after World War I, when he moved to Würzburg.

In his younger Reye publised works on physics and meteorology-for example, a book on cyclones (1872). The two-volume first edition of his emetrie der lage appeared in 1866 and 1868. He remained faithful throughout his life to the synthetic geometry presented in this work. His interest in geometry had been stimulated by analytical mechanics,and Culmann, the founder of graphic statics, had drawn his attention to Staudt’ work on geometry Staudt’s book were considered very difficult to read;Reye’s Geometrie der Large, the fifth edition of which appeared in 1923, was easily comprehended.

Reye treated in detail the theory of conics and quadrics and of their linear systems, that of third degree surfaces and some of the fourth degree, as well as many quadratic congruences and aggregates taken from line geometry. He was one of the leading geometers of his time, and he published a great dealon systhetic geometry. His to the axial complex of a second-degree surface, and generalized the polarity theory of algebraic curves and surfaces, introducting the concept of apolarity.

Reye was the founder of that portion of projective geometry that E. A Weiss later called point-series geometry. In a series of writting,Reye treated liner mainfolds of projective plane pencils and of collinear bundles or speace. Later these investigations were easily interpreted multidimensionally by means of the geometry of Segre manifolds Reye refused to speak of true geometry when dealing with space of more than three dimmensions. He was satisfied to interpret multidimensional relations in P2 and p3, that is, he treated the geometries. In 1878 Reye published a short work on spherical geometry, the only one of his mathematical writings, besides the Gemetreic der lage, to Apear as a separate publication. An important configuration of twelve points, twelve plants, and sixteen lines in P3 is named for Reye.


I. Original Works. Reye’s writing include die Geometrie der large, 2 vols. (Leipzig, 1866–1868), 5th ed., 3 vols. Leipzig, 1923);Synthetische Geometrie der Kugeln (Leipzig, 1879); “Über algebraische Flachen, die zueinander apolar sind,” in journal für die reline and angewandte methematik, 79 (1874), 159–175; and 211–240; 106 (1890), 30–47, 315–329; 107 (1891), 162–178; 108 (1891), 89–124.

II. Secondary Literature. See C. F. Geiser, “Zur Erinnerung an Thedor Reye,”;in Viereljahrsschrft der Naturforchenden Gesellschaft in zürich66 (1921), 158–160; C.Segre,“Cenno commemorativo di Reye,” in atti dell’ (1922), 269–272; and H.ETimerding, “Theodor Reye,” in jahresbericht der deuschen mathematiker- Vereingung,31 (1922), 185–203.

Werner Burau