On 2016-08-17 08:30, Tom Rokicki wrote:
Wow, Mathematica can do that?
Yeah but it took 9 minutes.
Thanks, Bill, very nice!
It's 20 times faster if you do it floatingly, but sometimes you get dandruff: gosper.org/icosaisagon.png And sometimes you don't.
On Wed, Aug 17, 2016 at 7:18 AM, Bill Gosper <billgosper@gmail.com> wrote:
Pending the discovery of some high-powered Mathematica solution, you could always display the full-res B&W polygon next to an el-crudo winding number color legend: gosper.org/pentadecagon.png (Where turns[L_List] := Total[Mod[RotateLeft[#] - # &@Arg@L + π, 2π] - π]/2/π .) --rwg
On 2016-08-16 06:27, James Propp wrote:
I agree with Allan: pictures that show the different winding numbers around different regions should be in the final write-up, and using color might give some very nice pictures. But there's a non-trivial programming problem here. Are there any off-the-shelf graphics packages that play nicely with reentrant polygons?
Tom's pictures remind me of the Klein disk model, and so I am led to wonder: do all these closed paths that encircle signed area zero retain the zero-signed-area property if we replace the line segments by circular arcs perpendicular to the boundary? (I guess there are two flavors of this question, depending on whether you measure Euclidean area or hyperbolic area.)
Jim Propp
On Wednesday, August 10, 2016, Allan Wechsler <acwacw@gmail.com> wrote:
It would be glorious if you could color-code the different winding-numbers, so we could see the +1's and -1's balancing (as well as the occasional 2's and 3's).
On Wed, Aug 10, 2016 at 1:19 PM, Tom Rokicki <rokicki@gmail.com <javascript:;>> wrote:
The images show in my email, not sure why you aren't seeing them.
The following link should work:
https://docs.google.com/document/d/1G3FL1Pcc8RgZ0DZOxibSonMGSJtrYOc6OUwXjThE... [Bogus linebreak removed. And probably reinstalled by xmission.com.] --rwg
-tom