Mathematical models
Three-dimensional models that give tangible, visible form to the properties of surfaces, solids, singularities, and other objects treated in mathematics. They were produced in great numbers under the direction of mathematicians, chiefly in Germany, from the late 19th to the early 20th century, made of plaster, metal, glass, and other materials, and spread to universities in many countries as teaching aids. In Japan, the University of Tokyo holds a collection of models imported up to around the First World War, which is also known through the photographs of them by the photographer Hiroshi Sugimoto.
History
Around 1870 the mathematician Kummer presented a model of Steiner's Roman surface. From the 1870s onward, model-making projects were pursued in Germany, centered on Klein, Brill, and others, with the firm of Martin Schilling undertaking production. Schilling ceased producing models in 1932.
What they represent
They represent the shapes of surfaces defined by equations, such as the Roman surface, the Clebsch surface, the pseudosphere, the Kuen surface, and cubic surfaces, and the geometric properties around special points called singularities.
The University of Tokyo collection
The plaster and other models held by the Graduate School of Mathematical Sciences at the University of Tokyo are said to have been imported, during or before the First World War, by Senkichi Nakagawa, who was on the staff of the Department of Mathematics in the Faculty of Science from 1904 to 1937. Since March 2013 about 100 of them have been on permanent display at Intermediatheque, and from April to July 2015 several models were also exhibited at the Mori Art Museum.
Hiroshi Sugimoto's works
The photographer Hiroshi Sugimoto has presented works photographing the 19th-century mathematical models held by the University of Tokyo. They were made with an awareness of precedents: Marcel Duchamp's inquiry into space, and the photographs of mathematical models that Man Ray took at the Institut Henri Poincaré in Paris in the 1930s. Sugimoto went further and produced mathematical models of his own as sculptural works, feeding the equations into a computer and milling them from solid aluminum on precision machine tools. A collection of these works, Conceptual Forms and Mathematical Models, was published by Hatje Cantz in 2015.
To verify
- Where Sugimoto photographed the models (one source gives the Komaba Museum of the University of Tokyo) and when
- The main exhibitions in which Sugimoto's mathematical model works were shown
- The name of the 2015 exhibition at the Mori Art Museum in which the models were displayed
References
- Mentioned in
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