Faculty Mentors: Karen Mortensen (Director of the Illinois Mathematics Lab), Sarah Park (Head of the Mathematics Library)
Project Leader: Xinran Yu (Ph.D. candidate in the Dept of Mathematics)
IML Scholars: Joules Apura, Dashiell Cloud, Dylan Jenks, Wentao Qi, Jadzia Taborski
Michael Dalton: Manager, CU Community Fab Lab
Kyungwon Koh: Director, CU Community Fab Lab
The University of Illinois is home to one of the world’s largest collections of historical mathematical models, comprising approximately 400 pieces dating from the late 19th to early 20th centuries. The collection includes models purchased from Germany, as well as those designed and built by faculty and students in the Department of Mathematics.
The history of mathematical models at the University of Illinois dates back over a century. Edgar Townsend, the second chair of the Department of Mathematics (1905–1928) and former dean of the College of Science (1905–1913), recognized the unique value of mathematical models, from transforming abstract mathematical formulas into three-dimensional objects for research to helping students visualize geometric concepts through tangible representations. To support these goals, he acquired mathematical models and related books from overseas. Arnold Emch (professor of mathematics at Illinois 1911-1939), took the work a step further by designing and building additional original models here, with the help of mathematics students and publishing descriptions in the University of Illinois Bulletin. Emch’s contributions significantly enriched both the collection and mathematics education at the University of Illinois.
The collections of mathematical models are not just objects—they represent the dedication and vision our faculty invested over a century ago in advancing education and research.
The renovation of Altgeld Hall has presented a unique opportunity to study these historical materials and potentially revive and expand upon these efforts in the 21st century.
The models were originally created to give students hands-on experience with mathematical concepts that were rapidly becoming more and more abstract. Because physical models are both valuable and somewhat fragile, transporting them and demonstrating their functions poses a challenge students are not able to handle them as originally intended. As a result, the idea of recreating them using 3D printing was explored. This approach not only allows for the production of durable plastic replicas but also makes it possible to share the digital design files (STLs) with others—potentially extending the reach of the project beyond the local community. It also provides students with a valuable opportunity to gain first-hand experience with 3D printing technology.
After searching for a lab, the CU Community Fab Lab, led by Dr. Koh of iSchool, was recommended. Just a few days after initial contact, Lab Manager Michael Dalton generously offered students guided tours and access to equipment for hands-on learning and experimentation. The student group had the opportunity to explore a variety of tools and materials available at the Fab Lab, gaining exposure to different media and fabrication techniques.
Students explored various techniques to visualize mathematical formulas and created 3D printouts for demonstration using tools such as Wolfram Mathematica and Autodesk Fusion 360. They spent many hours working in the lab, monitoring prints and refining their models using special software. This process gave them a deeper understanding of the mathematics behind the models. They spoke excitedly about their work with historical mathematical models, noting that—with the support of the staff and leadership of the CU Community Fab Lab—the models can now reach a wider audience than ever imagined through digital modeling and 3D printing.
Dr. Karen Mortensen, who leads the Illinois Mathematics Lab, spoke of the excitement she felt upon discovering that the lab offers so much to both students and community members, and she highly recommended it to students interested in experimenting with geometric models and other mathematical concepts. “I’ve seen that although students enjoy studying images of the historical math models and learning the mathematics behind them, their degree of engagement and their level of understanding really shoots up when they have the chance to examine and (carefully) touch the models. This is exactly why the models were first created! With the options for affordable 3D printing at Fab Lab, we can create reproductions that will allow many more people to have this same experience.”
Sarah Park, Head of the Mathematics Library, underscored that collaboration with the CU Community Fab Lab opened up new opportunities for recreating historical objects through digital modeling and 3D printing. This collaboration allows for a wider dissemination of the University’s historical mathematical models. She expressed her gratitude for the knowledgeable staff at the lab and their invaluable support of the student research project.
Figure 1 shows the 3D model generated in Wolfram Mathematica using a mathematical formula, while Figure 2 displays the actual 3D-printed output.
