I think you have your function mixed up ! x,y / x,y would equal less density as you would be stretching out the matter involved in your scenario . You could of said xzy/xy = <z as an oblate .
What about degenerate triangles? All 3 points degenerate points can be on a circle, they represent a transposition and appear in 2 dimensions as a linear sequence. https://undergroundmathematics.org/glossary/degenerate Also consider Gonal numbers where each n-gonal number can be decomposed into the sum of a triangular number.