Dr. Silviana Amethyst is a visualizing mathematician at the University of Wisconsin-Eau Claire. Her favorite subjects are singular algebraic surfaces. Lately, she's been getting into hybrid printed and electronic projects. Silviana's love of the Barth Sextic knows no bounds. She rejects white supremacy in all forms.

Lecture #5: Augmenting 3D printed objects for interactivity

3D printing is a wonderful way to illustrate mathematics. We get tangible objects. By augmenting them with additional features, we can make our pieces interactive. This talk will present a family of similar objects, with various features for interactivity. The major addition to the plastic is electronics, powered by a student-programmed Arduino. By adding effort beyond the build platform, we gain access to a world of projects for show, outreach, and teaching.

David Bachman is a professor of Mathematics at Pitzer College in Claremont, CA. He received a PhD in 1999 from the University of Texas at Austin, and has since published over 20 research articles, three books, and received two grants from the National Science Foundation. Eleven years ago, David's background in mathematics and his affinity for working with his hands converged when he began to experiment with 3D printing. Since then he has created unique two and three-dimensional pieces by using several CAD modeling packages (most notably, Rhino 3D and Grasshopper), a variety of laser cutters, pen plotters, and 3D printers, and a garage full of tools. David is a certified Rhino specialist (Levels 1 and 2) and has written a book on Grasshopper, the visual scripting plug-in for Rhino.

Lecture #6: Tutorial of model design and Workshop #2

This tutorial will demonstrate the software and tools used to take a mathematical idea, describe it analytically, and encode it as a 3D model. We will discuss three main approaches and tools for model creation: programmatic generation (scripting), mesh based sculpting, and NURBS modeling. The presentation will conclude with ideas and suggestions for the next workshop.

Gabriel Dorfsman-Hopkins (he/they) is an RTG Postdoctoral Scholar at the University of California, Berkeley, specializing in arithmetic and p-adic analytic geometry. They also have research interests along the intersection of art and math, working with 3D printing, fiber arts, and electronics, with an interest in interactive models and installations. Before arriving in Berkeley, Gabriel was a postdoc in residence at ICERM for the semester program titled "Illustrating Mathematics." Gabriel received their PhD from the University of Washington in 2019, with a dissertation exploring foundations of perfectoid geometry, and while at UW, they managed the digital fabrication lab space in the Washington Experimental Math Lab.

Lecture #3: Tutorial and demonstration of 3D printing software and tools and Workshop #1

In this talk we will give a down to earth demonstration of how to use an extrusion-based 3D printer, going through an entire example of how to turn a digital model into a physical one. We will go through the process of preparing a model for printing, explaining how to make sure a digital model is printable, and giving tips on how to recognize and troubleshoot common issues that arise.

Elisabetta (Sabetta) Matsumoto is an assistant professor in the School of Physics at Georgia Institute of Technology. Her physics research centers around the relationship between geometry and material properties in soft systems, including liquid crystals, 3D printing and textiles. Her lab studies knitted textiles from the point of view of knot theory and as an additive manufacturing technique. She is also interested in using sewing, 3D printing and virtual reality in mathematical art and education.

Lecture #4: Mathematics and challenges behind 3D printing

3D printing is still a developing technology that faces many challenges, mainly mechanical, material, computational and algorithmic. The process of printing can be divided into three steps each offering its own mathematical problems: model design, preparation for printing via slicing and infill algorithms, and physical process of layer deposition in the printer. Optimizing these steps for printing time, cost, and physical qualities of the final product drives many challenges in this area. The printing processes itself can be quite complicated and prone to error. A common problem is a loss of alignment leading to splitting layers. Error correcting for such issues is an active field of research involving automatic feedback mechanisms and machine learning. Materials and dynamic properties of printed objects (i.e. their 4D behavior) are fundamental to successful uses in both industry and research. The goal of this lecture will be to introduce and explain approaches to these problems and discuss open questions and ideas.

Henry Segerman received his master's in mathematics from the University of Oxford, and his Ph.D. in mathematics from Stanford University. He is an associate professor in the Department of Mathematics at Oklahoma State University. His research interests are in three-dimensional geometry and topology, and in mathematical art and visualization. In visualization, he works in 3D printing, spherical video, virtual reality, and augmented reality. He is the author of the book Visualizing Mathematics with 3D Printing.

Lecture #1: Visualization of mathematics with 3D printing

I will give an overview of the many uses of 3D printing in mathematical visualization and mathematical art. These include works illustrating symmetry, polyhedra, projections of higher-dimensional objects, fractals, knots, and surfaces. I will also discuss generative work coming from dynamical systems and computational biology. Finally, I will talk about mechanisms and puzzles, both of which take advantage of the physicality of 3D printed objects to give experiences that cannot be matched by computer generated renders and animations

Bethany Weeks has been passionate about the additive manufacturing (AM) industry for almost a decade. She was a founding member of the University of Washington's 3D printing student group and helped create the world's first 3D printed full-sized boat using 100% post-consumer plastic as material. She is currently an engineer performing research in AM at Boeing Additive Manufacturing (BAM), identifying the capabilities of the technology and releasing design guidance for how to incorporate AM into production. Prior to Boeing, she was a R&D engineer at Stratasys, tasked with optimizing the printing parameters for new materials and FFF systems.

Lecture #2: Introduction to 3D printing

In this talk we will discuss the history of 3D printing and the revolutionary shift to additive manufacturing (AM), which differs dramatically from traditional manufacturing, allowing for fast prototyping and production of small or complicated pieces. Current applications include industry, dentistry and medicine (crowns, custom hearing aids, implants, prosthetics), footwear, architecture, aerospace and home products. In addition, AM is considered to be more eco-friendly than traditional because it uses material more efficiently. The lecture will include a detailed discussion of the variety of printer designs (extrusion, stereolithography, selective laser melting, etc.), fabrication materials (plastic, plaster, metal, glass, ceramic and even food), and solidifying process (drying, laser cut, and thermal.

Timea Tihanyi is a Hungarian born interdisciplinary visual artist and ceramist living and working in Seattle, Washington. Tihanyi holds a Doctor of Medicine degree from Semmelweis University, Budapest, Hungary and an MFA in Ceramics from the University of Washington. Tihanyi’s work has been exhibited in the United States, Brazil, Australia, Denmark, Spain and the Netherlands. Tihanyi is a Teaching Professor in the Interdisciplinary Visual Arts program at the University of Washington. She is the founder and director of Slip Rabbit, a unique mentoring space for experimentation and learning with ceramic 3D printing at the intersections of art, design, architecture, math, science and engineering. Tihanyi collaborates with mathematicians frequently. She is the author of Making and Breaking Rules, a Technoceramist's Adventures with Mathematical Thinking. Her latest exhibition, Object Permanence, will open on January 21st, 2022 at the Bellevue Arts Museum.

Panel #2: Discussion with the speakers on 3D printing, research, and art