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You mock, but this kind of tinkering is basically the foundation of mathematics. I suggest reading Lockhart's Lament, linked on this Wikipedia page: https://en

You mock, but this kind of tinkering is basically the foundation of mathematics. I suggest reading Lockhart's Lament, linked on this Wikipedia page: https://en.wikipedia.org/wiki/A_Mathematician%27s_Lament https://en.wikipedia.org/wiki/A_Mathematician%27s_Lament Relevant quote: > For example, if I’m in the mood to think about shapes— and I often am— I might imagine a triangle inside a rectangular box. I wonder how much of the box the triangle takes up? Two-thirds maybe? The important thing to understand is that I’m not talking about this drawing of a triangle in a box. Nor am I talking about some metal triangle forming part of a girder system for a bridge. There’s no ulterior practical purpose here. I’m just playing. That’s what math is— wondering, playing, amusing yourself with your imagination.

Udo 12y ago
Aside from its style, this seems like a valid criticism. How trivial can a permutation be and still be sufficiently interesting for someone to (justifiably) slap his name on it? That said, this was still a nice read and the guy is obviously having fun with it, so good for him.
- Gelada 12y ago
  In this case the change is significant. If you just cut squares you can do quite a bit and it leads to significant ideas related to continued fractions, but you will only get finite continued fractions (rational numbers) and periodic ones (quadratic numbers). Cutting rectangles and squares can give higher degree algebraic numbers, like the cubic number for the main spiral. I am working on a porrf that you can get all algebraic numbers.