Students at the University of Illinois Urbana-Champaign have embarked on an innovative project to create 3D models of mathematical surfaces and theorems. This initiative, led by the Illinois Mathematics Lab and the Champaign-Urbana Community Fab Lab, allowed undergraduates to recreate a selection of historic models, some dating back to the 1800s. The project utilizes FDM printing, and the newly created models are part of a 400-piece collection owned by the university’s mathematics department.
The collection features visual representations of complex theorems originally constructed from materials like plaster, wood, cardboard, and metal. Many of these models were designed at Illinois and were previously used in classrooms. Notably, the originals were imported from Germany, contributing to one of the largest collections of mathematical models globally. Mathematics librarian Sarah Park emphasized the significance of this collection, stating, “These are a department treasure. They offer unmatched educational value to students and researchers alike.”
Recent renovations in the mathematical department, Altgeld Hall, necessitated the relocation of the original models from storage, leading to a unique opportunity for students. They documented, studied, and digitized the historic pieces, rendering them in 3D using software tools like Mathematica alongside slicing programs. The printed models, made with plastic filament, represent various mathematical constructs, including a conic section-proof Dandelin sphere, a Kummer surface, and other ruled geometrical shapes. Accompanying descriptions allowed students to delve into the foundational equations anchored in historical texts, many originally written in German.
These new mathematical 3D printed models are intended for educational outreach within the Urbana-Champaign community, extending their use into middle and high schools. Compared to their fragile predecessors, these models provide a more durable, hands-on learning experience that digital tools and simulations cannot replicate. The original models will continue to be preserved in the university archives, with a digital archive in progress that will feature high-resolution photographs, written descriptions, and downloadable 3D model files for educators and researchers.
This project reflects an exciting convergence of technology and education, where preserving mathematical history ensures these models remain accessible for future generations. For more information and to access the digitized collection of math models, visit HERE.