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FebruaryThis time I have one excellent new essay for you: Sums of Cubes.
I also have an amusing story about the not-so-excellent essay The Pentagon Knot. I started work on it months ago, just after finishing the previous batch in fact, but then some other things came up. Then, last month, when I got excited about Sums of Cubes, there were some related subjects that I wanted to know more about, so I did a bit of mathematical reading. First I tried Sphere Packings, Lattices, and Groups, a book that I bought years ago, that I wish I could understand, but that's just too dense and advanced for me. I didn't have much luck this time either, but I did at least figure out that I really ought to read Regular Polytopes first. So, I picked up a copy of that, and there as the first sentence of the second paragraph I found this.
Everyone is acquainted with some of the regular polygons: the equilateral triangle which Euclid constructs in his first proposition, the square which confronts us all over the civilized world, the pentagon which can be obtained by making a simple knot in a strip of paper and pressing it carefully flat, the hexagon of the snowflake, and so on.
So, it's no longer true that I've never seen the pentagon knot mentioned in print. I decided to let that bit of the essay stand, though, and just tell the whole story here. Isn't that a strange coincidence?
@ February (2011)