Dithering

Dec. 28th, 2018 11:16 am
stoutfellow: Joker (Joker)
[personal profile] stoutfellow
I've had some time to think about the Varignon idea, and it's every bit as interesting as I hoped. It behaves in half a dozen different ways, depending on certain easily determined factors; at least some of the time, it provides a link between two things that I knew had to be connected, but couldn't define the connection until now.

One fact that I've run into repeatedly in my study of polygons: if the number of sides is odd, one set of phenomena occurs; if it's a multiple of four, a sharply different set occurs; and if it's neither - if it's even, but not a multiple of four - what happens is sort of a hybrid of the other two cases. This trichotomy recurs as regards the Varignon transform, and in most cases the result is somewhere between "Hmm, that's interesting" and "Wow!".

I really really want to start writing this stuff up, but it *has* to wait until I write the paper on isolated classes. Unfortunately, I keep changing my mind about how to structure that paper; I'd hoped to finish before the end of last summer, but now my best shot is to get it out the door by the end of the next semester.

:is frustrated:

Profile

stoutfellow: Joker (Default)
stoutfellow

April 2020

S M T W T F S
    1 2 34
5 6 789 1011
12 13 14 1516 17 18
19202122232425
2627282930  

Most Popular Tags

Style Credit

Expand Cut Tags

No cut tags
Page generated May. 24th, 2025 02:07 pm
Powered by Dreamwidth Studios