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Presenting...
Jun. 11th, 2015 06:32 pmToday I had to go onto campus to take care of some paperwork. While I was doing this, W dropped in, and I asked him if he had some free time to listen to the stuff I've been researching the last couple of months. We spent something like an hour going over it; he asked good questions and made appropriate appreciative noises.
Mathematicians are artists. We need to show off our work sometimes.
Now I need to start writing it up. I'd made a tentative outline of the papers to be written, but what I've discovered in the last couple of months blew that to bits. I've redesigned the plan, but I'm still a little anxious about it. The work involves setting up a great deal of machinery, in two big chunks; I'm going to have to separate those, because there are limits to how much machinery-building someone will sit through before demanding that you do something with it.
So, the first paper will lay out the first big chunk of machinery, and then use it to analyze triangles. There are some very interesting things that don't happen in triangles, but on the other hand I can put together an arguably complete discussion of triangle classes in a reasonably short time.
The second paper takes a breather from machinery-building, and goes after some low-hanging fruit, displaying and analyzing about two dozen classes of quadrilaterals, pentagons, hexagons, and octagons. All of these classes have a particular property that makes them of special interest, and they're the only classes with that property.
The third paper constructs the rest of the machinery, showing how to describe infinitely many possibly-interesting classes, for polygons with any number of sides, and identifying some properties of some of those classes. This, I'm still working on; I've got a few results, but completism demands more.
Gotta buckle down to work.
Mathematicians are artists. We need to show off our work sometimes.
Now I need to start writing it up. I'd made a tentative outline of the papers to be written, but what I've discovered in the last couple of months blew that to bits. I've redesigned the plan, but I'm still a little anxious about it. The work involves setting up a great deal of machinery, in two big chunks; I'm going to have to separate those, because there are limits to how much machinery-building someone will sit through before demanding that you do something with it.
So, the first paper will lay out the first big chunk of machinery, and then use it to analyze triangles. There are some very interesting things that don't happen in triangles, but on the other hand I can put together an arguably complete discussion of triangle classes in a reasonably short time.
The second paper takes a breather from machinery-building, and goes after some low-hanging fruit, displaying and analyzing about two dozen classes of quadrilaterals, pentagons, hexagons, and octagons. All of these classes have a particular property that makes them of special interest, and they're the only classes with that property.
The third paper constructs the rest of the machinery, showing how to describe infinitely many possibly-interesting classes, for polygons with any number of sides, and identifying some properties of some of those classes. This, I'm still working on; I've got a few results, but completism demands more.
Gotta buckle down to work.
