Jodi Heckel
June 27, 2025
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Sarah Park and Karen Mortensen in front of the Mathematical Models collection.
Mathematics librarian Sarah Park and director of the Illinois Mathematics Lab Karen Mortensen are surrounded by historical mathematical models owned by the Illinois math department. It has one of the world’s largest collections of such models, which depict abstract mathematical principles in a three-dimensional way. Mortensen and Park supervised a student project to recreate some of the models using a 3D printer. Photo by Fred Zwicky

CHAMPAIGN, Ill. — University of Illinois Urbana-Champaign students recreated some of the historical mathematical models owned by the U. of I. math department using a 3D printer.

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Original math model with 3D printed recreation.
This moveable model offers a dynamic proof that the cross-section of a cone (at a suitable angle) is an ellipse. The spheres are called “Dandelin spheres.” Students 3D-printed a re-creation of the model, which the Illinois Mathematics Lab can use for its outreach activities to area schools. Photo by Fred Zwicky

The Illinois math department has nearly 400 mathematical models — one of the world’s largest collections — from the late 19th and early 20th centuries. The models demonstrate abstract mathematical principles in a three-dimensional way. Many of them were purchased around the turn of the century from the German company Martin Schilling, and others were designed and built by Illinois math professors.

“They are a department treasure,” said mathematics librarian Sarah Park. “We have the largest collection of these objects, and they offer a unique value to mathematics scholars on campus as well as around the world.”

The models were displayed throughout Altgeld Hall, which houses the math department. Moving them to storage during the ongoing renovations of Altgeld Hall offered an opportunity to catalogue and recreate the models. Students worked on the project through the Illinois Mathematics Lab, which offers undergraduate opportunities for mathematical research, experimentation and visualization. They used the Champaign Urbana Community Fab Lab to make the new models.

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