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My Polyhedra Textbook, I – Creativity in Mathematics
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…
My Polyhedra Textbook, II – Creativity in Mathematics
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…
The Fourth Dimension, IV – Creativity in Mathematics
In the past few weeks, we looked at the hypercube in four-dimensional space. We approached this intriguing geometrical object using thinking by analogy; that is, we looked at one-, two-, and three-dimensional hypercubes (segments, squares, and cubes), and imagined potential properties -- such as the number of vertices, edges, faces, and cells -- of a…
Polyhedra Graphics, I – Creativity in Mathematics
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,…
The Fourth Dimension, I – Creativity in Mathematics
I have found that the topics of infinity and the fourth dimension really do always pique students' interest. When I had a few moments left at the end of a class period, I could sometimes casually remark about one of these topics, and I immediately had the attention of the entire classroom. One of my projects…
The Fourth Dimension, III – Creativity in Mathematics
Last week we counted vertices, edges, faces, and cells on a hypercube. Mainly, we thought by analogy -- but how could we be sure our intuition was correct? Today, we look at another say to make these same counts, and obtain the same results. This suggests that maybe we were right all along.... So we…
Largest Number Found! – Creativity in Mathematics
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 --…
The Fourth Dimension, II – Creativity in Mathematics
Last week, I introduced the idea of a fourth spatial dimension. The typical question students ask is simply, "Where is it?" These doesn't seem to anywhere it can go -- and in fact, since we live (insofar as we know it) in a three-dimensional world, there really isn't anywhere it can go. So the fourth spatial…
Recursively Generated Spirals – Creativity in Mathematics
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…
The Puzzle Cabaret – Creativity in Mathematics
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…