How do you visualize something which doesn't fit on a page, like a high dimensional space or an entire field of math? You lie and cheat, use shortcuts and shorthand. In this talk, I'll share my favorite tips and tricks for bringing math to life in digital painting.

# Seminar

The Illustrating Math Virtual Seminar meets the second Friday of each month. Talks cover a wide range of topics related to successes and challenges of mathematical illustration, from cutting edge theoretical research to explorations of intersections between mathematics and the arts. The seminar showcases innovative ways to communicate and explore deep mathematical ideas.

The monthly seminar is held on Zoom. Each meeting opens with two five-minute ‘show and ask’ style presentations (volunteer here to give one), which are followed by the main feature, a 40 minute invited colloquium talk. Immediately afterwards, participants (and speakers) are invited to gather informally on the illustrating math discord server for further social interaction.

The Illustrating Mathematics Seminar Online celebrates the life and work of Roger Antonsen.

The theoretical discovery of hyperbolic geometry first got its actual tactile example in 1868 when Eugenio Beltrami created a negatively curved surface from paper annuli and named it *a pseudosphere*. Later the name *pseudosphere* got attached to a surface created by a tractrix rotating around its axis. However, mathematicians found more useful for theoretical purposes using different, non-tactile models such as Klein or Poincare disc models or half-plane model. Those are traditionally used in college textbooks. However, to experience deeper understanding of hyperbolic geometry, these models were not enough for Bill Thurston when he was a college student. Since in 1901 Hilbert proved that hyperbolic plane cannot be described analytically in 3-space, Thurston together with his peers at informal seminar decided to make a tactile model of hyperbolic plane and created it by gluing together paper annuli without knowing about Beltrami’s paper model created hundred years earlier. I learned about Thurston’s model in 1997 and decided to make it more durable by crocheting it. Crocheted hyperbolic planes have turned out to be a useful tool in tactile explorations of hyperbolic geometry giving to theoretical knowledge a different perspective.

I'll tell a few mathematical stories from my personal experience with mathematical illustration as a research tool in number theory, sharing some of my experience with the process, not just results. Topics include Apollonian circle packings, Mobius transformations, continued fractions, and algebraic integers.

I'll tell a few mathematical stories from my personal experience with mathematical illustration as a research tool in number theory, sharing some of my experience with the process, not just results. Topics include Apollonian circle packings, Mobius transformations, continued fractions, and algebraic integers.

When most people picture mathematical art, they envision regular shapes formed by plotting precise equations. In this talk, I will discuss my approach to creating art through a very different process, where mathematics is used to guide a virtual growth process. The results frequently mirror shapes found in nature, both in form and aesthetic appeal.

Nelson Max will show segments of several computer animated films from the 1970s, on turning a circle or sphere inside out by a regular homotopy, and on space filling curves, and demonstrate a web-based system for uniform tilings of the sphere, plane, and hyperbolic plane.

I’ve been illustrating mathematics since I’ve known any, and will be showing a variety of work in a range of media.

I'll talk about my work in mathematical visualization: making accurate, effective, and beautiful pictures and models of mathematical concepts. I'll discuss what it is that makes a visualization compelling, and show many examples in the medium of 3D printing.

PLEASE NOTE THE UNUSUAL TIME OF THIS MONTH'S MEETING!

By combining mathematics, technology, and craft we can produce physical and visual artifacts that help us discover and explore new ideas. We'll discuss a range of topics from knot theory to the fiber arts, and use code, 3D printing, and vintage punch card knitting machines to create pattern generation tools and physical models that illustrate and clarify the underlying mathematics. We'll also discuss the ups and downs of design processes that include challenges that arise from intersecting mathematics, technology, and crafting.

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