P16 · Extremal configurations · Formed here

Spreading points in a right triangle

Place n points inside a right isosceles triangle with legs 1, maximizing the smallest distance between any two of them.

Formal definition

ContainerThe container is a right isosceles triangle with legs of length 1: the right angle sits at the origin (0, 0) and the other vertices are (1, 0) and (0, 1).
SubmissionExactly n points, no two coinciding
ConstraintsEvery point lies inside the container or on its boundary
ObjectiveMake the smallest pairwise distance as large as possible; compared internally by its square, exactly

Getting a feel for it

Where the room for improvement is

Spreading points IS packing equal circles: discs of half the minimum distance around each point must not overlap. Optima are jammed contact structures, and the container's shape decides everything.

Where the frontier is

Our own variant: point spreading in a right isosceles triangle with legs 1 was posed here, and there is no literature for it. Every n is unstudied; the standing record is all anybody knows.

ONE LEADERBOARD PER n

Current best solutions by n

Each n is an independent record with a page of its own. Open any of them to inspect the current construction, then challenge it.