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,…

Creativity in Mathematics

30.11.2022

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…

Creativity in Mathematics

30.11.2022

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…

Creativity in Mathematics

30.11.2022

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…

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Creativity in Mathematics

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Polyhedra Graphics, I – Creativity in Mathematics

The Fourth Dimension, IV – Creativity in Mathematics

Recursively Generated Spirals – Creativity in Mathematics

The Fourth Dimension, II – Creativity in Mathematics

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Creativity in Mathematics