23 Apr

Pythagoras Cubed

I was recently invited at the last minute to lead a mathematical construction for a seminar for math majors at Loyola Marymount University. The hope was to create something physical connected with one of the topics in the course, which linked the history of mathematics with various unsolved problems, among other things. Since there had been a fair amount of discussion about the Pythagorean Theorem, we settled on the following construction that demonstrates an interesting and less-familiar related phenomenon in three dimensions.

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12 Apr

New Call for Problems

I serve as the Problem Warden for the Prison Math Project (PMP), meaning I edit The Prisoner’s Dilemma, the quarterly problem section of the PMP newsletter. So I’d love it if you have intersting problems or mathematical puzzles to submit to the column. Of course, you will be credited online and in the newsletter for any problems you submit.

I also welcome solutions to the existing problems from anyone. Problems range in difficulty from high-school contest level up to roughly the easiest end of Putnam competition problems. So to submit problems or solutions, please email me at dilemma “at” pmathp “dot” org. Looking forward to your ideas!

09 Apr

Truncated Triakis Tetrahedron

For the actual building event mentioned in the previous post (linked above), participants could choose from a variety of target polyhedra. The origami inspiration was the PHiZZ unit, which stands for Pentgons Hexagons in Zig Zag, so the ideal targets consist of just pentagons and hexagons. With Euler’s formula for polyhedra and a little calculation you can determine that such a shape must have exactly twelve pentagons and almost any number of hexagons; the page for the event includes a table of candidates.

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08 Apr

Modular Origami, without the origami

In many ways, modular origami is ideally suited for the type of exploratory mathematical play that S∞ is dedicated to: it’s easy to get started, very tactile, and offers nearly endless opportunities for creating interesting and beautiful objects. For example, here’s a PHiZZ unit torus that resulted from a workshop I led at The Brearley School (photo courtesy of Maggie Maluf).

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23 Mar

Summer 2021 PCMI Illustrating Math

This post was for announcing a week-long summer workshop on Illustrating Mathematics at the Park City Mathematics Institute, this past 2021 July 19-23. It was an exciting week with lots of interesting programming including several different hands-on, how-to tutorials, keynotes by Vernelle Noel, Ingrid Daubechies, and Daniel Piker, and mathematical “show-and-ask” sessions in which a wide array of mathematicians displayed some of the intriguing and beautiful images and objects they’ve created, as well as highlighting the questions these projects have raised. (I led one minicourse on using CAD/CAM software like LibreCAD or FreeCAD in creating physical mathematical models.)

12 Mar

Wirecosahedra

When I showed this recent post to my friend and colleague Laura Taalman, aka mathgrrl, she suggested that another approach to creating a model of the underlying structure would be to construct the icosahedra themselves (rather than the negative space), except use wireframes of the icosahedra rather than solid ones to avoid obscuring all of the internal structure. Her encouragement motivated me to create a new OpenSCAD file for this.

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09 Mar

Anticos

Judging from at least one of the previous projects, Studio Infinity is intrigued with connecting polyhedra edge-to-edge. (Of course, connecting them face-to-face is interesting, too, but that’s pretty familiar from Legos and such; and vertex-to-vertex is the same as connecting dual polyhedra face-to-face.)

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