Angela Vierling-Claassen: Models of Mathematical Surfaces

Schools and Museums with Models

This is a list of schools and museums which have some models of surfaces. Please send me an email (angelavc"at symbol"math.harvard.edu) if you know of a school or museum which has mathematical models but is not listed here.

Centro de Matemática e Aplicações Fundamentais (CMAF - University of Lisbon)

The CMAF has copies of models of ruled surfaces from the Conservatoire des Arts et Métiers made around 1864, and they has working reproductions made. They used to have a webpage up about the models, but that seems to have dissapeared.

Conservatoire des Arts et Métiers in Paris (France)

The Conservatoire had a series of string models in 1830 (according to Fink p.277). They still have many interesting objects, including models of surfaces, many by T. Olivier. See their catalogue (in French).

Eberhard Karls Universität Tübingen

Has several photographs of Brill/Schilling models online. According to their website, Alexander Brill was a professor of math at Tübingen which lead to the development of their collection.

Fairfield University in Connecticut (US)

Seems to have some -- the website for Joseph F. MacDonnell, S.J. contains pictures and analysis of some models.

Harvard University in Cambridge, Massachusetts (US)

Harvard has a number of plaster models from the Brill/Schilling catalogues in a glass case in the mathematics department. The case in on the fourth floor of the science center, in the math department lounge.

Martin-Luther-Universtät Halle-Wittenberg (Germany)

Their web page (in German) on the history of the mathematics department has an item for their historical collection of mathematical models, but links have not been provided.

Massachusetts Institue of Technology in Cambridge, Massachusetts (US)

There are models in cases at MIT in the mathematics building (building #2). These models have recently been restored by the mathematics department and I am working on cataloging them. The models are mainly plaster models from the Brill catalog (although there are a couple of Schilling models).

Poincare Institute in Paris (France)

Man Ray photographed some of the models at the Poincare Institute. The library says that they still have over 400 models, some of which are on permanent display (and a couple of which are pictured on the website). See their web site.

The Science Museum in London (UK)

In 1876 there was an exhibition of scientific apparatus at the South Kensington Museum, which eventually became the Science Museum. Many mathematical models were exhibited, and the museum still has a large collection. Henry Moore was inspired by models at the science museum (see Henry Spencer Moore, p. 105.) A summary of the museums mathematics collection mentions models of surfaces, there is an online exhibition of surfaces as well, and other photos of surfaces can be found in the Science and Society Picture Library. Jane Wess is the curator of Mathematics and astronomy, j.wess@nmsi.ac.uk. See the references list for books on the collections.

Smithsonian Institute, Washington DC (US)

Has a pretty extensive collection of models in the Division of Information Technology and Communications , but only a couple were on display the last that I was there. Peggy Kidwell curates the mathematics collection -- follow the link above for contact information if you want to make an appointment to study the collections. There is a virtual exhibit titled Slates, Slides, Rules, and Software: Teaching Math in America that contains some models.

Union College (US)

Union College has a large collection of models built by T. Olivier. They have an impressive display online, including a program you can download to explore the models, videos of the models, and a history of the models.

Technischen Universität Dresden (Germany)

Has a great collection of over 400 models some of which are viewable online. According to their website, the collection was established after World War II, but they were able to aquire a large number of models from the Martin Schilling publishing house when it went out of business in 1960.

Università degli Studi di Torino (Italy)

According to it's website, the applied math department has a collection of 180 models of various different makes (but many from the Brill/Schilling catalogs). There is a very nice complete catalog in italian online maintained by Nicla Palladino.

Universität Regensburg (Germany)

Has an online display of models, both historic and modern.

University of Arizona (US)

The mathematics department has a great web site on thier collection with lots of pictures. Many of their models were made by R. Baker.

University of Groningen (Netherlands)

This university, along with several others in the Netherlands, have a number of models and have put up a nice collection online. This collection is terrific because there are photos, organized by series in the Schilling catalog, along with extensive information about each model.

University of Illinois at Urbana-Champagne (US)

Has an outstanding collection in Altgeld Hall, discussed here.

University of Napoli (Italy)

The Mathematics Department has a collection of Schilling models. There is an online catalog maintained by Nicla Palladino.

University of Tokyo (Japan)

The University of Tokyo, Graduate School of Mathematical Sciences, has a collection of models that are said to have been imported from Germany by Prof Senkichi NAKAGAWA around 1910. You can find some photos and other information on their website. Thanks to Yoshiaki ARAKI (who is involved in modeling of 3D quasi-fuchsian fractals) for the tip. Photographs of some of the models in this collection appeared in New York Times Magazine.

Wellesley College (US)

Wellesley has a number of (approx 50) models of polyhedra in plastic. Some has stickers saying "A. Harry Wheeler" on them, and I suspect that all were from a collection created or sold by Wheeler. They had a couple of plastic models showing intersections of surfaces that had stickers saying "Unterrights Modelle" and that they were made in Germany. There were five stringed models of ruled surfaces with aluminum frames. There were two larger string models. One, in metal, looks like something I've seen in Dyck's catalog, so I have to look at that again. The other, made of wood, I think depicted a cone and a hyperboloid of one sheet. The string on that model was unravelling quite a bit.

Kidwell has a photograph showing some Brill models at Wellesley College (photo pub in "Women in the American Mathematical Community" in Math Intelligencer 1987 #9 p 17, in Wellesley College Archives).

I have a copy of the Wellesley College Bulletin for the 1925-26 school year that notes (p. 144), "The [mathematics] department has a collection of 45 Brill-Schilling models of surfaces, chiefly of the second and third orders, beside [sic] several simple models, including some made by its members."

Other Sites of Interest Relating to Models

Universal Joint Design: Jonathan Chertok has been recreating a number of models using rapid prototyping and other technologies and has a great website about the project.