Illustration
I am interested in illustrating mathematical concepts through computer graphics and 3D fabrication. Below are links to some projects along these lines.
Undergraduates interested in working on an Honors Program research project can feel free to email me.
Non-Euclidean Paper
I make non-Euclidean “paper” by thermoforming sheets of plastic onto 3D printed surfaces. I focus on the potential of these models as teaching tools for studying non-Euclidean geometry and differential geometry. Here are links to my Bridges 2023 proceedings article, and the project page.
Three Points of Defect
My submission to the Polyplane exhibition (2023, video), "Three Points of Defect" illustrates a genus-zero polyhedron with only three vertices of nonzero angle defect using origami. For more details, see the accompanying project page.
Together with Janet Chen, I worked on a project to design and produce 3D models to be used in active learning lessons in multivariable calculus courses at Harvard University.
Se our project website www.manipulativecalculus.com for information on the models, and details on the project.
Flat Klein bottle sculpture
A curved-crease origami sculpture of the "flat" Klein bottle. This is the image of a Klein bottle with zero Gaussian curvature meant to preserve most of its geometry and topology.
A full explanation available in my Bridges 2021 paper. See also my interview in Physics Magazine.
Californians love to complain about how they get the fewest Electoral College votes per capita. But is that really the best way to think about their voting power? I made this YouTube video to illustrate different ways of thinking about how power is distributed among states in the Electoral College (and to the individual voters in those states).
This video was my submission to the SoME1 contest.
In Fall 2019, I participated in the ICERM semester program in "Illustrating Mathematics". I got to work with mathematicians from around the country on illustrating various mathematical concepts using an assortment of media including 3D fabrication, computer graphics, and virtual reality. My focus at the program was thinking of ways to illustrate mathematics to undergraduate students.
Embedded hyperbolic tilings project page
Hyperbolic paper project page
Desmos Applets
Here are a few Desmos applets I have used in classes I've taught and for talks I've given. Here are a few of my favorites.
On my Thingiverse site @stepanp21, I have posted even more 3D print designs (in addition to most of the designs listed above). A few favorites:
Miscellaneous
"Spectral Snub" public build (with Glen Whitney)
