
 
Caption: Mathematical Models by Arnold Emch  Series 3 (1925) This is a reducedresolution page image for fast online browsing.
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K 5 H PREFACE ^ The mathematical models listed and described below } have been planned and designed in the mathematical labor\ atory of the University of Illinois since the publication1 of thefirstseries in 1921 and the second series in 1923. A s has been stated in thefirsttwo series, the purpose of these constructions is to represent certain features of mathematical instruction and research by adequate models, mechanisms, or graphs, which are not available in the market. In the second series four models are described which illustrate the connection between the apparent doublepoints and the genus in case of an important class of spacecurves, those sextics, which are obtained as intersections of quadric and cubic surfaces. In the n e w series models are presented which exhibit similar features in case of quartics of thefirstkind. T h e theory of surfaces is represented by a cubic, a quartic, and a quintic. T h e latter is a special example of a class of generalized cyclides, whose properties were studied by Dr. H . P. Pettit. References to these surfaces will be found in the text. Particular interest m a y be attached to the model, illustrating geometrically the properties of the symmetric substitution group of order 24. It is believed to be thefirstof its kind in existence. For those interested in models as listed in series I, II, and III, arrangements can be m a d e with private firms for the manufacturing and sale of duplicates. For further information, especially concerning the procuring of duplicates, apply to Arnold E m c h , Associate Professor of Mathematics, University of Illinois. University of Illinois Bulletin, Vol. XVIII, No. 12, formally dated Nov. 22, 1920; and Vol. X X , No. 42, June 18, 1923. jV)'3kVn>
 