Art in the library    color palette    אמנות בספריה

Mathematical models display      תצוגת דגמים מתמטיים

The library's collection of mathematical models includes The models are exhibited permanently in the library at the entrance area.
"Mathematical model" / Encyclopaedia Britannica Online.
Physical mathematical models include reproductions of plane and solid geometric figures made of cardboard, wood, plastic, or other substances; models of conic sections, curves in space, or three-dimensional surfaces of various kinds made of wire, plaster, or thread strung from frames; and models of surfaces of higher order that make it possible to visualize abstract mathematical concepts.

Schilling models of surfaces

The Göttingen collection of mathematical models and instruments was developed to use physical models and experimental instruments in education and research. This model collection already had a long history when Hermann Amandus Schwarz and Felix Klein overtook the direction of the collection.

The model collection was systematically modernized and completed for the education in geometry and geodesy under the direction of Klein. This collection was considered so important that Klein exhibited the models on the occasion of the World s Columbian Exposition 1893 in Chicago.

Most of the models were produced by Martin Schilling in Leipzig. The firm's catalogue of the firm catagorized the models into series. Each model is described and explained.
Martin Schilling : Catalog mathematischer Modelle für den höheren mathematischen Unterricht. 7. Aufl. Leipzig : Martin Schilling,1911.

These models inspired artists, particularly Man Ray, who was inspired by the Mathematical models at the Institut Henri Poincaré, Paris, shown to him by the artist Max Ernst.
Man Ray - Human equations = מאן ריי משוואות אנושיות , an exhibit on his "Shakespearean Equations" was on display at the Israel Museum October 22, 2015-January 23, 2016. The exhibit included some models from our collection.


The Library's collection of Schilling mathematical models

Prof. Felix Klein's personal collection was purchased in 1927 by Prof. Edmund Landau for the mathematics library.
This collection included some mathematical models made of gypsum (Prof. Klein had rearranged and added to the collection of mathematical models in Göttingen).
For more information, see: → Library's history.

Other collections of Schilling mathematical models

Collections of Schilling mathematical models exist in several mathematical institutions around the world. Some of the following websites also include additional information on the models and their classification.    See also: Collections of mathematical models  /  Angela Vierling-Claassen, Department of Mathematics, Lesley University

Click on a small image to see the larger picture

Schilling classification Description in German from catalog Library model English description More information from other collections
Series XVI, designed 1888 by Prof. E.R. Neovius
Göttingen classification: A.I.g. Confocal systems.
A confocal system describes conic sections with the same foci respectively their body of rotation.
XVI no.1 Ellipsoid mit drei Hauptschnitten und achtzehn Krümmungslinien Schilling model 16.1 Ellipsoid with three basic intersections and eighteen lines of curvature University of Groningen
XVI no.4 Einschaliges Hyperboloid Schilling model 16.4 Single-leaf hyperboloid with a family of lines Göttingen Model 388
XVI no.5 Zweischaliges Hyperboloid Schilling model 16.5 Double-leaf hyperboloid Göttingen Model 26
XVI no.6 Vereinigung eines Ellipsoids mit einem confocalen einschaligen Hyperboloid Schilling model 16.6 Single-leaf hyperboloid and confocal ellipsoid
Union of an ellipsoid with lines of curvature (coming from intersecting confocal quadrics) and a confocal single hyperboloid (with two families of lines)
Göttingen Model 27
XVI no.7 Vereinigung eines Ellipsoids mit einem confocalen zweischaligen Hyperboloid Schilling model 16.7 Ellipsoid and confocal double-leaf hyperboloid
Union of an ellipsoid with lines of curvature (coming from intersecting confocal quadrics) and a confocal double hyperboloid
Göttingen Model 29
XVI no.8 Vereinigung eines einschaligen Hyperboloids mit einem confocalen zweischaligen Hyperboloid Schilling model 16.8 Single-leaf hyperboloid and confocal double-leaf ellipsoid.
Union of a single hyperboloid with a confocal double hyperboloid
Göttingen Model 28
XVI no.9 Vereinigung eines Ellipsoids mit einem confocalen einschaligen und einem confocalen zweischaligen Hyperboloid Schilling model 16.9 Ellipsoid, confocal single- and double-leaf hyperboloid.
Union of an ellipsoid with a confocal single hyperboloid and a confocal double hyperboloid
Göttingen Model 30
Series XXIII, designed 1889
XXIII no.1b. Das dreiaxige Ellipsoid mit Krümmungslinien Schilling model 23.1b Triaxial ellipsoid with lines of curvature
XXIII no.3 Das zweischalige Hyperboloid Schilling model 23.3 Double hyperboloid Mathematischer Modelle an der Technischen Universität Dresden
XXIII no.5 Das hyperbolische Paraboloid Schilling model 23.5 Hyperbolic paraboloid with planar cut Göttingen Model 7

Great ditrigonal icosidodecahedron Great ditrigonal icosidodecahedron

M.C. Escher kaleidocycles

Also displayed in the library, polyhedral forms assembled from the book:
M.C. Escher Kaleidozyklen / von Doris Schattschneider und Wallace Walker.
Berlin : Benedikt Taschen, 1990.
Translation of M.C. Escher kaleidocycles.

M.C. Escher Kaleidozyklen      Escher models

More information:
M.C. Escher  /  Wikipedia

Conic sections and polyhedra models in plastic

Plastic models

Models photographed by: Gila Manusovich-Shamir, Jerusalem
© 2009, All rights reserved.

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Last updated: April 17th, 2016