Students Bring Mathematical Models to Life Using 3D Printing

Students at the University of Illinois Urbana-Champaign have created new 3D models of mathematical surfaces and theorems. In a project spearheaded by the Illinois Mathematics Lab and the Champaign-Urbana Community Fab Lab, undergraduates at the university were able to recreate a selection of the university’s historic models with some dating to the 1800s, using FDM printing. The models are part of a 400-piece collection owned by the university’s mathematics department.

The collection itself includes visualizations of complex theorems constructed from plaster, wood, cardboard and metal. Many of the pieces were designed by an Illinois facility and previously used for classroom instruction and demonstration. The original pieces were imported from Germany and are part of one of the world’s largest collections of mathematical models. Mathematics librarian Sarah Park noted, “These are a department treasure. They offer unmatched educational value to students and researchers alike.”

Student-created version of Dandelin spheres [left] with original wooden model [right].

Due to recent renovations at the university’s mathematical department, Altgeld Hall, the original models were taken out of storage. This relocation offered students a unique opportunity to document, study and digitize the historic models. Students were then able to select models and utilize software tools such as Mathematica and slicing programs to render them in 3D. The new models were then printed at the CU Community Fab Lab using plastic filament and optimized printing settings. Some of the re-created models include a conic section-proof Dandelin sphere, a Kummer surface, and other ruled surfaces using taut threads. Students were tasked with creating descriptions to accompany each newly printed model which allowed them to study the original equations from sources written in German.