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Seminar on the History of Mathematics
May 4, 2017 18:00, St. Peterburg

The history and modernity of mathematical models of Martin Schilling’s catalog

G. A. Kuteeva

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Abstract: In the late 19th century, outstanding German mathematicians Eduard Kummer, Felix Klein and Alexander von Brill became one of the inspirers of a visual demonstration of mathematical abstract facts. Ludwig von Brill (1844-1932), brother of Alexander von Brill (1842-1935), became one of the organizers of the manufactory in Darmstadt for the manufacture of mathematical models. (L. Brill's manufactory began work in 1880). Initially, these were plaster models of various surfaces, for example, the surface of rotation of the tractory with geodesic and asymptotic lines, the surfaces of the centers of curvature of the main sections of the same-sex hyperboloid, geodesic lines on the surface of the ellipsoid of rotation, and others. Further the manufactory also produced wire and cotton models on copper machine tools and substrates, series of kinematic models appeared. These models were buying by higher educational institutions of various countries, including Russia, America, Italy and others. Such a plot is interesting. At the World Exhibition in Chicago in 1893, F. Klein presented a gypsum model of the Clebsch surface, a third-order surface on which there are exactly 27 real straight lines. In his lectures during the exhibition Klein insisted on the importance of creating such models for the development of intuition and as an instrument to combat the excessive abstractness of mathematics. In 1899 the manufacture of L. Brill was purchased by Martin Schilling and moved to Halle, and then to Leipzig. As early as 1911, the catalog of Schilling manufactory contained 40 series of models that included more than 400 items. Mass sales in Europe and America continued until the early 30's. Most of the old universities in Europe have acquired extensive collections of models of Schilling and other publishers. At the same time, the models were actively used both in the scientific and in the teaching activities of scientists. The report proposes to show the pages of the catalog of Martin Schilling (two editions: 1903, 1911), on which various series of mathematical models are presented. It is offered to look the modern Internet sites of universities of different countries with collections of mathematical models of the Martin Schilling catalog. In St. Petersburg University, some models of this catalog from the kinematic series are also preserved, these are moving visual mechanisms. The report will feature photos and some student animations of these mechanisms.

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