Stephen K. Lucas, Evelyn Sander (of the GMU Math Makerlab), and Laura Taalman wrote an article about how to practically 3D print actual physical models of such dynamical structures. This appeared in an article in the American Mathematical Society Notices in December 2020 (cover image shown is a 3D printed model from the article). An adapted version appeared in the book The Best Writing on Mathematics 2021, Princeton University Press.

In Fall 2021, GMU Math 401 Mathematics Through 3D Printing created iterated function systems.

Fall 2021 GMU Mathematics Through 3D Printing, Pentagon Tiling Assignment: A student’s rendition of one of the Reinhardt 1918 planar pentagon tilings – method for automated suburb creation? OpenSCAD code modified from one by mathgrrl.

In Fall 2021, GMU Math 401, Mathematics Through 3D Printing created mathematical optical illusions. These are objects such that the shape look totally different in the mirror. In each case, you are looking at an object and its mirror image. A diamond becomes a crescent moon, a batman symbol is rightside up both in reality and in the mirror. How does it work? Mathematics! And a clever idea by Sugihara.

In Fall 2021, GMU Math 401 Mathematics Through 3D Printing printed their favorite mountains.

About the Lab

The goal of the GMU Math Maker Lab is to use 3D printing technology to turn abstract mathematical concepts into concrete physical objects. Seeing and designing prints allows for better understanding and enthusiasm for mathematics!

Activities include research, teaching, outreach, tutorial development, as detailed below. The lab is housed in a room within the math department on the 4th floor of Exploratory Hall on the George Mason Fairfax Campus. Activities are directed by Prof. Evelyn Sander with the aid of GMU graduate and undergraduate students. For more information see the old GMU Math MakerLab Blog.

Teaching

• Math 401: Mathematics Through 3D printing (capstone course), every fall starting in 2019
• Math 493: Mathematics Through 3D Printing, Spring 2016
• Math 213: Multivariable Calculus, Spring 2015

Research

• Sublevel sets of spinodal decomposition for the Cahn-Hilliard equation, a nonlinear partial differential equation
• Construction of self-similar tiling

Tutorials

• Modeling Dynamical Systems for 3D Printing, AMS Notices article
• Construct3D talk February 2020
• An overview of 3D printing and tutorials on how to begin.

Outreach

• Booth at the USA Science and Engineering Festival 2018
• Mathematics in Motion Booth, Maker Faire NOVA, 2018
• Math Circle Presentations, GMU, 2015, 2016, 2017, 2018
• Speed dating event, Active Learning Seminar, GMU, October 27, 2016. Infographic
• Booth at the USA Science and Engineering Festival 2016
• GMU FOCUS STEM Camp July 2015
• Presentation for Middle School Girls Visit to the GMU AWM Chapter April 2015
• Technology and Innovations Conference September 2015

Equipment

• Makerbot 5th Generation PLA printer
• Makerbot 2X dual ABS printer
• Lulzbot TAZ5 multi-material printer with dual extruder
• Monoprice mini

Software

• Slicers: Makerbot Desktop, Simplify 3D, and CURA
• Design: OpenSCAD, Tinkercad, Mathematica, Paraview, Sketchup, Matlab, C.

New 3D printed giveaways for campus events. Make sure you stop by the Math Department Booth!