Checkerboard

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Checkerboard

Postby dureisseix » September 14th, 2017, 2:18 pm

There have been a short discussion about the checkerboard (the board, not the chess pieces):
http://snkhan.co.uk/forum/viewtopic.php?f=5&t=3299&hilit=checkerboard#p28670
but this post concerns a more general challenge: folding the nxn checkerboard from a single square sheet of paper with one color per face. Additionnaly, the question is: what is the optimal design (i.e. the smallest initial square for the same folded design)?
An old (2000) upper bound on the paper size has been stated in
https://hal.archives-ouvertes.fr/hal-01380815
It has been outperformed (2009) in
https://dspace.mit.edu/openaccess-disseminate/1721.1/62156
but only for n > 16. Since then, there have been several effectively folded models of the expected optimal chessboard (n=8), but I have not seen real models folded for a larger n.
So, here is my latest attempt: the 11x11 checkerboard
Image
from a 60x60 paper (half-folded to feel the complexity).
The design principle is not new, and is described in
https://arxiv.org/abs/1510.07499
but the real physical folding may well be.
So, the question is:
the effective folding of the optimal 11x11 checkerboard (i.e. from the smallest initial square of paper - not proved but strongly suspected), is it a world record??
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Re: Checkerboard

Postby anonymous person » September 14th, 2017, 5:49 pm

This is really fascinating work - have you considered submitting a paper to 7OSME? http://osme.info/7osme/
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Re: Checkerboard

Postby dureisseix » September 15th, 2017, 10:02 am

For the submission to 7OSME, the answer is definitely: yes. The working document on arxiv was made for steering me to work on it. Moreover, this is 9-year delay discussion (2000, 2009, now 2018 for 7OSME...)
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