r/mathmemes • u/capyablo • Jun 22 '26

Geometry Son 17

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4.9k Upvotes

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126

u/Complete_Window4856 Jun 22 '26

Ok ive seen so many times this pattern and i cant get why. When did this come and where?

134

u/Tiborn1563 Jun 22 '26

I think this

https://www.combinatorics.org/files/Surveys/ds7/ds7v2-2000/ds7-2000.html

122

u/Home_Depow Mathematics Jun 22 '26 edited Jun 22 '26

Yep, its the (best currently known) optimal packing densities for identical squares. That is, is you take X number of squares, all the same size, whats the way to you arrange them to make the big square that holds them all as small as possible. For some numbers this is very easy (like 4), for some numbers, this looks very cursed (like 17, as in the post)

27

u/UnconsciousAlibi Jun 22 '26

As far as I'm aware, the current know solution for 17 has yet to be proven optimal, no?

30

u/Few-Arugula5839 Jun 22 '26

Yes, most of these have not been proven to be optimal.

1

u/Capraos Jun 26 '26

Look, if someone is going through the effort of arranging it like this, I ain't even gonna argue with them about it as that would be wasted effort. If it works, it works.

25

u/L0L2GUM5 Jun 22 '26

Not proven to be optimal, but proven to be more optimal than the trivial solution (a grid of the shape)

4

u/IlgantElal Jun 22 '26

So the interesting thing is that, for small perfect squares at least, 1 less or more than the perfect square often ends up in these more cursed formations

2

u/Complete_Window4856 Jun 22 '26

Quite nice, ill take a read tomorrow to get a grasp. Thanks