[seqfan] partitions of a circle
Neil Sloane
njasloane at gmail.com
Tue May 8 05:57:26 CEST 2012
Dear Sequence Fans, There is a paper:
*Valette, G.*; *Zamfirescu, T.* Les partages d'un polygone convexe en
4 polygones
semblables au premier. (French) *J. Combinatorial Theory Ser. B* *16 *(1974),
1--16. MR0331217 <http://www.ams.org/mathscinet-getitem?mr=0331217> *(48
#9551),*
*see **http://www.sciencedirect.com/science/journal/00958956/16/1,*
*which studies the ways to divide a polygon into 4 congruent pieces.
*
But they begin by looking at a simpler question:
the number of ways to divide a circle into 4 pieces: there are 15 ways,
according to their rules. Similarly, I think there are 4 ways to divide a
circle into 3 pieces.
So there is a sequence 1, 1, 4, 15, ... I can't tell yet if it is in the
OEIS. I scanned in their
illustration of the 15 partitions into 4 pieces, and I will be happy to
send it to anyone
who wants to try to help find the next couple of terms.
The 4 ways to cut a circle into 3 pieces are:
1. draw 2 parallel chords in a circle
2. draw a T in a circle
3. draw a Y in a circle
4. draw a V in a circle
Neil
--
Dear Friends, I will soon be retiring from AT&T. New coordinates:
Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com
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