Heilbronn's Problem (first rised about 1950):

For a given convex set in the Euclidean plane of area 1, e.g. the unit square,
place n points inside, such that to maximize the area of the smallest triangle
defined by any three of the points.

It it said (see R.K. Guy et all) that this problem is the continous analog of
the discrete no-three-in-line problem.

In the no-three-in-line problem the area for a given n x n grid should be 1.
Therefore for each fixed n we have to scale the grid by a factor of 1/n in
both axes.
Next we can obviously place at most 2n points. It is conjectured that for
sufficient large n this number will be always less than 2n.

But let us restrict n to atmost 70, to be sure we can meet the no-three-in-line
condition with 2n selected points. Now the analog question to Heilbronn's
question should be: How to place the points, such that to maximize the area
of the smallest triangle defined by any three of the points?

Let us call this area value depending on n, the critical value of n.

For n <= 16 the critical value is 1/2. And for all known no-three-in-line
configurations with n <= 16 (even for all known configurations independent of n)
 this is true, too.

Therefore  we have 1/(2n^2) as the area of the minimal triangle.

This was Heilbronn's conjectural answer to his problem, too. But it was
1982 disproved and shown to be > log(n)/n^2 for sufficient large n.

see URL https://en.wikipedia.org/wiki/Heilbronn_triangle_problem