[seqfan] Portolan Numbers
ebeihl at gmail.com
Tue Nov 29 18:49:49 CET 2016
Cf. my recently-published A277402 and recentlyer-submitted A278823; also
my OEIS wiki user page <https://oeis.org/wiki/User:Ethan_Beihl>.
In the last month or two, I've been researching the number of regions
obtained by n-secting the angles of a regular polygon (some pictures
I call these the "portolan numbers" equally for the pun and for their
connection to the mapmaking technique.
I'm new to SeqFan and I don't know what interests you all have, but I
suspect this might tickle one or two fancies -- take a look and please
investigate if you feel compelled. The underlying math is essentially
the theory of trigonometric diophantine equations, but I've only
actually *found* and solved the equation given by the m = 3 case.
Finding the equations is a job for a geometer, while an algebraic mind
like mine is perhaps more suited to solving them. If you're up to the
challenge, let's start looking for a complete trigonometric
characterization of the concurrencies of lines in these figures!
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