Second Look
May. 11th, 2018 04:25 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stoutfellowMan, I'm glad I assigned my (now ex-) Master's student that project.
There is a phenomenon which involves certain classes of polygons with an even number of sides. I noticed it some years ago; it's noticeable with quadrilaterals, and more strongly with hexagons. I tried investigating it in general - for all evengons - but it didn't behave the way I wanted it to, or in any useful way at all, so I dropped the subject.
In her investigation of hexagons, my student noticed the phenomenon, and made heavy use of it. We talked about it some, and I began thinking about it again. This time, with the additional tools I'd developed, I was able to see just why it worked in the cases she'd looked at, why it misbehaved in general, and - this is important - how to identify the cases in which it didn't misbehave. (There are infinitely many of them, so there's lots of meat on those bones.) The tools I used are going to be the main subject of Taxonomy III and IV. Even so, I can - without those tools - explain why it works with quadrilaterals, hexagons, and octagons, and I'll be able to include that much in Taxonomy II.
I may have to reshuffle the order of topics in III and IV, so I can include this stuff in III. But that's a way off - I've got to write Taxonomy II first!
There is a phenomenon which involves certain classes of polygons with an even number of sides. I noticed it some years ago; it's noticeable with quadrilaterals, and more strongly with hexagons. I tried investigating it in general - for all evengons - but it didn't behave the way I wanted it to, or in any useful way at all, so I dropped the subject.
In her investigation of hexagons, my student noticed the phenomenon, and made heavy use of it. We talked about it some, and I began thinking about it again. This time, with the additional tools I'd developed, I was able to see just why it worked in the cases she'd looked at, why it misbehaved in general, and - this is important - how to identify the cases in which it didn't misbehave. (There are infinitely many of them, so there's lots of meat on those bones.) The tools I used are going to be the main subject of Taxonomy III and IV. Even so, I can - without those tools - explain why it works with quadrilaterals, hexagons, and octagons, and I'll be able to include that much in Taxonomy II.
I may have to reshuffle the order of topics in III and IV, so I can include this stuff in III. But that's a way off - I've got to write Taxonomy II first!
