Must stop trying to solve polynomial equations mentally while waiting at STOP signs ... WFL On Fri, Oct 11, 2019 at 1:19 PM Bill Gosper <billgosper@gmail.com> wrote:
On Thu, Oct 10, 2019 at 6:52 PM Bill Gosper <billgosper@gmail.com> wrote:
Remember that XKCD where they blindside a passing nerd with a paralyzing math puzzle? add what for the next one? <http://gosper.org/hepstop7.bmp>
SPOILER: StringReverse@"tsegral eht ot \"tepmurt\" tsellams eht gnitrevnoc ,nogatpeh fo )edis tsegnol( mottob tsniaga dettif esunetopyh htiw elgnairt thgir selecsosi ,neerG"
What is the scale ratio of consecutive stopsigns?
In this Recoloring <http://gosper.org/hepstop8.bmp>, let s be the overall arbitrary scale, and r be the scale ratio of consecutive triangles in the spiral.
In[265]:= s√2 == s r^7 + s r // Solve
Out[266]//InputForm={r -> Root[{-2 + #1^2 & , -#1 - #2 + #2^3 + #1*#2^4 + #2^5 & }, {2, 1}]} (composition of quadratic and quintic)
In[267]:= MinimalPolynomial@%[[1, 2]]
Out[267]= -2 + #^2 + 2 #^4 - #^6 + #^10 &
An "irradical" biquintic! With real root ~ 0.907461039808622 ~ 1/1.10197568394881 ("physically" measured by Brad).
And consecutive "trumpets"?
The guy behind you is honking his!
—rwg
Same ratio. Grow a trumpet to get next stopsign. —rwg These images were in ancient Macsyma dribblings. I must have numerically solved the biquintic, but I have absolutely no recollection of it. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun