Adam wrote: Bill 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, Actual value = ArcTan[(5 Sqrt[3])/11] ~ 0.666946 whereas 7 Pi/33 ~ 0.666398 That's a pretty massive difference. Indeed, it's closer to the even more implausible value of 2/3. In general, all of your swing angles will be arctangents of things in the quadratic field Q[Sqrt[3]], since they can be expressed as arguments of solutions to linear equations, the coefficients of which are complex numbers in the imaginary quadratic field Q[Sqrt[-3]]. The process of obtaining the equation and solution is pretty easy and boring. Sincerely, Adam P. Goucher http://cp4space.wordpress.com OMG, there really ARE 13 of them little goobers? gosper.org/flake13.png That's not so boring. --rwg 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
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