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… [Read more]

20 Apr

Three-D Pythagorean Theorem

This recent post described a construction that demonstrated the “Three-D Pythagorean Theorem.” Here we dive a bit deeper into this bit of mathematics that may be less familiar than it deserves. A right tetrahedron has, by definition, a vertex where three right angles meet (there can be only one). An example is shown in the… [Read more]

12 Apr

New Call for Problems

Hey, I have recently become the Problem Warden for the Prison Math Project (PMP). That means I’m the editor of 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… [Read more]

09 Apr

Tessellating Truncated Octahedra

With all of the recent activity at Studio Infinity on geometric units that can be automatically cut and scored, it was natural for the S∞ G4G14 giveaway to be the 14-sided Truncated Octahedron, which tessellates to fill space. The additional challenge here as compared to some of the earlier interlocking structures was to ensure that… [Read more]

09 Apr

Assembling a TTO

These are the assembly instructions for the Tessellating Truncated Octahedra; you’ll find background and the cut files for them on them in the following post. Materials Two TTO pieces per unit you wish to build The first order of business is to fully cut and punch out two of the pieces from the cut templates… [Read more]

09 Apr

More Non-origami Modules

Another aspect of the PCMI session on Illustrating Math was a series of exploratory, hands-on workshops. One of them focused, in part, on the design of modules like the one for the truncated triakis tetrahedron, but based on other existing modular origami units. It’s more or less possible to transpose any modular origami unit to… [Read more]

09 Apr

Truncated Triakis Tetrahedron

Materials 42 modular units cut out and folded (see Modular Origami, without the origami)(preferably 9 each of four colors and 6 of another) 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… [Read more]

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… [Read more]

04 Oct

Integer Complexity Measures

[Note this post is a bit outdated, and not maintained; the most up-to-date version of this information can be found in my pages on the OEIS wiki.] I’ve recently become interested in a family of interrelated sequences that can be found in the Online Encyclopedia of Integer Sequences (OEIS). These sequences all have to do… [Read more]

30 Aug

Whence 2/(3+√5) ?

In both the Woven SSD and the Woven GSD, you calculate the inset (from the points where the rods meet near their ends) for putting marks on the rods by multiplying their lengths by 2/(3+√5). Where does that strange-looking number come from? The key is that both figures consist of (regular) pentagrams, just interlocked in… [Read more]

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… [Read more]

23 Mar

Woven GSD

Materials Tools 30 equal-length rods Measuring Tape 32 rubber bands Scissors This is a sequel to a (pre-pandemic) post about weaving a stellated polyhedron. This time, I’d like to show how similar techniques can also be used to create a “great stellated dodecahedron” (“GSD” for short; illustration to the left). The materials are in fact… [Read more]