this was my favorite design, referencing the most ~~cursed~~ efficient way to pack 17 squares.
According to this article from 2009, the most efficient way to pack 17 squares into a square is still unknown.
Has there been a development since John Bidwell?
@realFedix @helge @nojus thanks, that says:
> The smallest case where the best known packing involves squares at three different angles is
n = 17.
> It was discovered in 1998 by John Bidwell, an undergraduate student at the University of Hawaiʻi, and has side length a ≈ 4.6756.
I wonder what Helge meant with 'since Bidwell'? Maybe that this is not proven to be optimal?
I wonder what Helge meant with 'since Bidwell'? Maybe that this is not proven to be optimal?
Simple answer: Yes. Bidwell's result is not proven to be optimal.
If you look at the survey, I linked, in particular the appendix, you discover that 4.445 < s(17) < 4.6757. Where s(17) is the optimal number for a 17 circle packing.
I am unsure how much computers have improved. My naive expectation would be that if somebody reimplemented the algorithm from here and wasted some money, they would get a better packing.
@nojus I just had a terrible idea ...
(anyone who wants to run with it or build on it, feel free to steal it)
@nojus Oh man, it *really* bothers me that they kept the double-size 0 and Enter when they could have made them square and keep the * and / keys... There are already 17 keys on a numpad!
Maybe that's part of the point, though.