Does this make sense or does it have holes in it? Trying to

>>7791583
how about at the midpoint on each side? that brings up the number of points to 19.

>>7791607

Oh ofc, I forgot that. Whoops.

So I guess you do something similar to step 3 but at the beginning, just to make sure that kind of thing doesnt happen.

File: Hexagon proof.png (178KB, 2050x1466px) Image search: [Google]

178KB, 2050x1466px

updated.

but what im really interested in isnt whether this works for this particular case, but whether the method would work for eveyr single question of the type:

"Fit X points into Y shape such that no two points are less than Z cm apart"

>>7791583
>>7791659
What do you do if I want points 11 units apart from each other?

19 is probably best in this case as you have stated, but you didn't prove anything yet

>>7791659
Generally triangular packing is the best. However there are counter-examples with weird or shapes

https://en.wikipedia.org/wiki/Circle_packing

>>7791684
You could put 1 on each midpoint to start.
Even if it were 10,000 cm, you could place one in the middle.
>>7791583
What if you changed "not less than" to "greater than (but NOT equal to)"?
That way you'd not be allowed to have them exactly 10 cm apart and would have to consider more interesting patterns, and look at how you can perturb a solution to your question into one where they have to be strictly less than 10cm away form each other.

>>7791707

oh man that really is interesting.

how would you even start working on a problem like that?

>>7791827
I have no idea.
Maybe something like deformation theory, calculus of variations and sphere packing?