I decided, finally, to take the big plunge. I’ve been steadily working on my polyhedra textbook (I’ve discussed this in My Polyhedra Textbook, I and My Polyhedra Textbook, II), but ran into a bit of a snag. Since I wrote those posts, I self-published The Puzzle Cabaret, and given what I learned in the process, decided to self-publish my polyhedra book. The snag? All my three-dimensional graphics are in color, and given that the book will approach 500 pages, would be prohibitively expensive to print in color. It would cost about $35 to print, but I want to sell it for less than that – the idea ..read more

I decided to undertake a new venture while staying home during the pandemic: write a puzzle book! I’m not sure how the idea ultimately condensed from a gaseous nebula of random ideas, but one thought was that with so many people at home now, they needed something fun to do. Why not puzzles? With several print-on-demand platforms available, I could even self-publish! If you’ve been following my blog from the beginning, you know I’ve written many posts about creating new and interesting puzzles. (You can search the index to easily find them.) And as a consumer of puzzle magazines for decades, I ..read more

Late last month, Professor Warren Porterdunk of Berryville University announced that he had, in fact, found the largest number.  I was lucky enough to arrange a virtual interview with him, which is summarized here. Of course, there is no largest number.  “That is the conventional mathematical wisdom, yes,” said Porterdunk.  “But when you include trans-transcriptional numbers — that is, numbers which cannot actually be written down — well, that’s a game-changer.”  Porterdunk calls these numbers Titans, derived from the acronym TTN, which he finds apt. So what ..read more

A few weeks, ago I dug out a problem which had puzzled me for over three years.  I finally decided that now it was time to really dig in — and to my surprise and delight, not only did I solve the problem, but I’ve already got a draft of a paper written!  The figure below is from that paper. The problem is yet another variation on the recursion which produces the Koch snowflake.  I discussed the Koch snowflake in one my first posts, so visit my Day007 post on this fascinating fractal for a refresher. So what is the variation here?  Consider the general recursive scheme where represents a for ..read more

In my last post, I talked about a textbook I had written to use in a course which, among other things, introduced students to a non-Euclidean geometry — spherical geometry.  And while the primary purpose of the text was for teaching a college-level course, the actual content of the text had a different origin. As I have mentioned previously, I got interested in polyhedra during graduate school, and was very fond of taking books about polyhedron models out of our mathematics library at Carnegie Mellon.  It was easy enough to photocopy the nets provided, or use the numerical data to construct ne ..read more

Now that I’ve moved on to semi-retirement, there is time to take on a 25-year-old project:  my textbook on polyhedra! I became interested in polyhedra during graduate school, when I was fascinated by the trio of books by Magnus Wenninger:  Polyhedron Models, Dual Models, and Spherical Models.  I don’t know how many times I checked out Polyhedron Models from the mathematics library at Carnegie Mellon University, but I have clear memories of flipping pages back and forth over and over again, trying to understand the various and subtle relationships among the 100+ models shown in the book. Of cou ..read more