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Comment by lacker | Hacker News Reader

Nice. This will come in handy the next time I need to fit 1846 equal circles into a single larger circle.

Maybe you're being facetious, but for a CNC operator they might find it useful in an unusual machining job- they probably stick with a hexagonal lattice and rectangular stock most of the time. Or a chip foundry might find it useful if they are maximize yields in a wafer of silicon.

It probably isn't immediately applicable to every single person's life but it might help some industries squeeze another 0.1% out of their production line. The free work presented here might cover a couple engineer's salaries once they find this website.

I feel like the more valuable thing would probably be the generalization of "fit as many of [irregular polygon] into the least number of length inches of material width X."

OTOH, there are a lot of these math toys that start life in the abstract and then end up finding extremely practical applications down the line— pretty sure that was the case for a lot of the dusty corners of linear algebra until 3D graphics was suddenly a thing and it all became super relevant very quickly.

I personally just used this to drill a bunch of vent holes, though N = 37.

It would make a cool series of posters.

It's interesting that beyond some number of circles the optimal solution likely always involves a regular equilateral grid in the center.

Also interesting that there are seemingly no solutions without loose circles beyond 91.

After hitting a high enough size ratio, the spaces leftover when you inscribe a hexagon (built from small circles) inside the large circle are basically always going to require filling with loose circles. It's probably provable, but I'm not sure how you'd actually go about it.

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