[k-man]

Inspired by superprismatic's puzzle here is a slightly different version

Place 7 points inside a square with a side length of 1, to maximize the distance between any two points. What is that distance? Points placed on the edge of the square are considered to be inside.

to place 4 points in the square you would place them in the corners and the distance would be 1

[Guest]

Cool puzzle.

I'd go with a perfect hexagon within the square, rotated a bit to get points on each edge, with the 7th point as the center. The distance between each point will be the same. (Sorry, too lazy to add values)

[Guest]

Cool puzzle.

I'd go with a perfect hexagon within the square, rotated a bit to get points on each edge (you'll have , with the 7th point as the center. The distance between each point will be the same. (Sorry, too lazy to add values)

Ok, did my calculations too late to edit my post. Pretty sure you get

0.5176

[curr3nt]

I get the same 0.5176 witha perfect hexagon.

Draw the hexagon with one of the "wheel axels" running along a diagonal.

The other two axels will be touching the square at a 75 degree angle. (Side connecting these two axels will be parallel to the axel along the diagonal creating a smaller 45-45-90 triangle. 180 degrees - 45 from this triangle and 60 from one of the hexagon triangles = 75.)

Using sin(75) = 1/h h = 1.0352 for the length of the axel. Divide by two to get the length of the hexagon sides and distance from points of the hexagon to the center.

Need more time to prove that a bigger perfect hexagon can't be made. But visually you are see trying to increase the length of the axel will start pushing two of the points outside the square.

[superprismatic]

I get .536 with the points (0,1), (.536,1), (.536,.464), (0,.464), (1,0), (1,.7321), and (.2678,0).

To within 3 significant figures, no two points are closer than .536.

[k-man]

Excellent job, superprismatic!

... than .536. The exact value is 4-2*sqrt(3) and is approximately 0.535898, but I'm just nitpicking.

[k-man]

marking it as solved