[seqfan] Portolan Numbers

Ethan Beihl 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 
here 
<http://ethan.beihl.org/erb/creative-work/mathematical-visualization/>. 
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!

Best,
Ethan


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