Re: [math-fun] Three flake frames
Bill wrote:
OMG, there really ARE 13 of them little goobers? gosper.org/flake13.png
That's not so boring.
I don't think so, unfortunately, if you're just rotating that portion of the Cl(flowsnake)\Int(Cl(flowsnake)) -- according to my calculations, the complex number solution has a modulus slightly different from 1 (so you'll need to rotate and enlarge). Can you zoom further into the centre of the design to check whether the correspondence is exact? Nevertheless, I can confirm that the second frame does work (but the angle is not 7pi/33). Sincerely, Adam P. Goucher
On Fri, Oct 4, 2013 at 10:06 PM, Bill Gosper <billgosper@gmail.com> wrote:
On Fri, Oct 4, 2013 at 9:52 PM, Bill Gosper <billgosper@gmail.com> wrote:
(Easy for YOU to say.) gosper.org/flakes.png First frame is swing angle π/3, confirming DanA's guess about trisected areas. 2nd frame is implausible swing angle 7π/33, or VERY nearly, showing subflake at a peculiar angle. 3rd frame is even weirder angle that seems to make a triskelion out of ten tiny flakes. Doubt this one.
Especially since they number thirteen.
--rwg
[...]
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On 2013-10-05 23:40, Adam P. Goucher wrote:
Bill wrote:
OMG, there really ARE 13 of them little goobers? gosper.org/flake13.png
That's not so boring.
I don't think so, unfortunately, if you're just rotating that portion of the Cl(flowsnake)\Int(Cl(flowsnake)) -- according to my calculations, the complex number solution has a modulus slightly different from 1 (so you'll need to rotate and enlarge).
Can you zoom further into the centre of the design to check whether the correspondence is exact?
Will do. Meanwhile, note http://gosper.org/flake13a.png . I didn't compute that arctan(7 √3/11). I just stumbled on it and it looked right. But not exactly, I agree. --rwg
Nevertheless, I can confirm that the second frame does work (but the angle is not 7pi/33).
Sincerely,
Adam P. Goucher
On Fri, Oct 4, 2013 at 10:06 PM, Bill Gosper <billgosper@gmail.com> wrote:
On Fri, Oct 4, 2013 at 9:52 PM, Bill Gosper <billgosper@gmail.com> wrote:
(Easy for YOU to say.) gosper.org/flakes.png First frame is swing angle π/3, confirming DanA's guess about trisected areas. 2nd frame is implausible swing angle 7π/33, or VERY nearly, showing subflake at a peculiar angle. 3rd frame is even weirder angle that seems to make a triskelion out of ten tiny flakes. Doubt this one.
Especially since they number thirteen.
--rwg
[...]
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (2)
-
Adam P. Goucher -
rwg