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Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.

2 votes
1 answer
326 views

How many lines of exactly n points can be placed in a discrete, square grid of size m x m?

Per the title, I'm seeking the definition of a function $f(n, m)$ which evaluates to the number of lines made from exactly $n$ points which can be placed on a two-dimensional discrete, square grid of …
Ben Burns's user avatar
  • 145
2 votes
1 answer
483 views

How many distinct sets of n collinear points are there in an evenly-spaced two-dimensional g...

I'm seeking the definition of some function $f(n,m)$ which evaluates to the number of distinct sets of $n$ collinear points which are selected from an evenly-spaced two-dimensional grid of $m \times m …
Ben Burns's user avatar
  • 145