Notes on History of Models

1. Look at this website on Rudolf Mehmke. Here is a rough (from altavista) translation of a paragraph from this web site:

   "Models, apparatuses, instruments: The conference of the German mathematician union (DMV) of the yearly 1892 took place in the autumn 1892 in Nuernberg following the conference of the society of German natural scientists and physicians. For this conference for the first time an exhibition of `models, apparatuses and instruments' was planned in the history of the DMV, for which Walther of Dyck of the technical university in Munich was responsible. The exhibition failed however 1892 because of the Choleragefahr, it took place however 1893 in Munich. In the introduction to the `catalog' Dyck referred to it: `he would like to think of the important aid, which the Mr. Boltzmann dedicated in Munich and Mehmke in Darmstadt on mathematical physics and on arithmetic relative departments haben' in the speciellen still. Indeed Mehmke had issued 18 own, even sketched and built objects and beschrieben."

   Should be able to find the above quote in Dyck's catalogue. Need to work on better translation.

2. According to Fink, construction of models of surfaces began in France, "in consequence of the example and actifity of Monge" (p. 277). Fink notes that in 1830 the Conservatoire des arts et metiers in Paris had a series of string models of second degree surfaces, "conoids and screw surfaces."

   Also according to Fink, Bardon "had plaster and thread models constructed for the explanation of stone-cutting, toothed gears and other matters." Another named Muret expanded this collection. Apparently such models were not of interest to mathematicians in France, but in 1876 Cayley and Henrici used these models in an exhibit of scientific instruments. (p. 277)

3. According to Fink, Plucker "brought together in 1868 the first large collection of models. This consisted of models of complex surfaces of the fourth order and was considerably enlarged by Klein in the same field." A wave surface was constructed in 1840 by Magnus (in Berlin) and Soleil (in Paris). (p. 277).
   
   
4. Fink: "At a meeting of mathematicians in Gottingen there was made a notable exhibition of models which stimulated further work in this direction." (p. 278). However, there is no mention made of the year.
   
   
5. A.Brill, Klein, and Dyck worked in the mathematical seminar of the Munich polytechnic school with model-building. According to Fink, from 1877 to 1890 more than 100 models were built.
   
   
6. Kidwell, p. 197.

   "The general increase in material abundance that has characterized the western world from the aighteenth century, accompanied by rapid changes in mechanical, electrical, and electronic technology, has brought with it a profusion of objects fulfilling mathematical functions."

7. Simple geometric models (cubes, prisms, spheres, cones, etc.) were recommended and used widely during the first half of the 19th century in the United states. Kidwell, p. 198-9.
   
   
8. Firms selling simple geometric solids: Holbrook School Apparatus Manufacturing Company, Claxton and Wightman (of Boston, 1835 catalogue), Benjamin Pike Jr. (of NY, 1850's, including conic sections), James W. Queen & Co (of Philly, 1859, including polygons, solids, and kits to make platonic solids, and models of polyhedra inscribed in glass cubes), W. Mitchell McAlister (of Philadelphia, 1869), J.W. Schermerhorn and Company (of NY, 1871), Baker, Pratt & Co (of NY, 1879), A.H. Andrews (of Chicago, 1881). Kidwell, p. 199.
   
   
9. Kidwell, p. 201:

   "Engel's book contained testimonials from Wolcott Gibbs of New York and the German mathematician G.P. Lejeune Dirichlet. Some of Engel's models survive in the Physics Collection of the University of Mississippi." Engel was hired to make drawings for the US Coast and Geodetic Survey, where he "also made plaster models of variations in the earth's magnetic field...One of these models survives at the American Philosophical Society and another at the Smithsonian."

10. "In 1857, 24 mathematically minded friends of Harvard University" bought copies of the Olivier models from Fabre de Lagrange. Upon their arrival, Benjamin Peirce had agreed to give a series of lectures on them. They remain today in Harvad's collection of scientific instruments. Olivier models were aslo purchaed by West Point, Students Institue of Technology, and Columbia School of Mines. Duplicates of the models were used at Princeton.

    Olivier gave a mostly complete set of his models to to Conservatiore in 1849. His remaining collected of forty models were sold after his death in 1869 to William Gillispie from Union College in Schenectady, NY, who exhibited them at Union College. After Gillispie's death, the models were sold to the college. Kidwell, p. 200.