Photo is by Matt Parker, with image manipulation by Henry Segerman

Photo is by Matt Parker, with image manipulation by Henry Segerman

Artist in Residence: 

Dr. Henry Segerman

World-Renowned Mathematician-Artist, Dr. Henry Segerman will be at Texas A&M University as a part of Artist in Residence Program of Academy for the Visual & Performing Arts of Texas A&M University on April 5-7, 2017. The lectures are free and open to the public.

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Dr. Segerman will give three public lectures at Texas A&M University.  His talks are always interactive and entertaining for all people who are interested in mathematics, art, design, architecture and computer science.
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  • Title: 3D Shadows: Casting light on the fourth dimension
    Where: HRBB 124
    Date and Time: Wednesday, April 5, 4:10pm – 5:25pm
    (As a part of CSCE 681 – Graduate Seminar)
  • Title: Design of 3D printed mathematical art
    Where: Scoates (SCTS) 208
    Date and Time: Thursday, April 6, 5:30pm – 6:30pm
    Title: Squares that look round
    Where: Architecture, Langford B (ARCB) 101 – Geren Auditorium
  • Title: Squares that look round
    Where: Architecture, Langford B (ARCB) 101 – Geren Auditorium
    Date and Time: Friday, April 7, 5:30pm – 6:30pm

Abstracts:

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3D Shadows: Casting light on the fourth dimension: Our brains have evolved in a three-dimensional environment, and so we are very good at visualizing two- and three-dimensional objects. But what about four dimensional objects? The best we can really do is to look at three-dimensional “shadows”. Just as a shadow of a three-dimensional object squishes it into the two-dimensional plane, we can squish a four-dimensional shape into three-dimensional space, where we can then make a sculpture of it. If the four-dimensional object isn’t too complicated and we choose a good way to squish it, then we can get a very good sense of what it is like. We will explore the sphere in four-dimensional space, the four-dimensional polytopes (which are the four-dimensional versions of the three-dimensional polyhedra), and various 3D printed sculptures, puzzles, and virtual reality experiences that have come from thinking about these things. I talk about these topics and much more in my new book, “Visualizing Mathematics with 3D Printing”.

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Design of 3D printed mathematical art: When visualizing topological objects via 3D printing, we need a three-dimensional geometric representation of the object. There are approximately three broad strategies for doing this: “Manual” – using whatever design software is available to build the object by hand; “Parametric/Implicit” – generating the desired geometry using a parameterization or implicit description of the object; and “Iterative” – numerically solving an optimization problem. The manual strategy is unlikely to produce good results unless the subject is very simple. In general, if there is a reasonably canonical geometric structure on the topological object, then we hope to be able to produce a parameterization of it. However, in many cases this seems to be impossible and some form of iterative method is the best we can do. Within the parametric setting, there are still better and worse ways to proceed. For example, a geometric representation should demonstrate as many of the symmetries of the object as possible. There are similar issues in making three-dimensional representations of higher dimensional objects.

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I will discuss these matters with many examples, including visualization of four-dimensional polytopes (using orthogonal versus stereographic projection) and Seifert surfaces (comparing my work with Saul Schleimer with Jack van Wijk’s iterative techniques). I will also describe some computational problems that have come up in my 3D printed work, including the design of 3D printed mobiles (joint work with Marco Mahler), “Triple gear” and a visualization of the Klein Quartic (joint work with Saul Schleimer), and hinged surfaces with negative curvature (joint work with Geoffrey Irving).

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Squares that look round: Spherical (or “360 degree”) still and video cameras capture light from
all directions, producing a sphere of image data. What kinds of post-process transformations make sense for spherical photographs and video? We can rotate the sphere, but is there an analogue to zoom in flat video? By viewing the sphere of image data as the Riemann sphere, we can use complex numbers to describe the positions of the pixels. By scaling the complex plane, we get something like a zoom effect, with which we can make a spherical version of the Droste effect. By applying other complex functions, we can “unwrap” the sphere, producing other Escher-like impossible images and video. The code to generate these effects is written in Python, and much of it is available on GitHub.

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Click here for more information about Henry Segerman
Click here to see Henry’s Maths Website
This lecture is free and open to the public!

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