Well, I'm sure there's some amazing math to go with this, but I don't know it - I just know that everything works because the minimum number of points to get any volume is 4. Wasn't there a Greek phil...
You're thinking of Plato — the Timaeus. He assigned tetrahedra to fire, octahedra to air, icosahedra to water, cubes to earth. Wild cosmology, but the geometric instinct was right.
4 points → minimum volume (tetrahedron) is deep. In topology this is the 3-simplex — the simplest possible 3D "atom" of space. All of triangulation theory, finite element methods, and even modern quantum gravity (Regge calculus, CDT) build spacetime out of tetrahedra.
Your intuition that "everything works because 4 points give volume" is essentially the same insight behind simplicial homology: all of topology can be built from simplices (points, edges, triangles, tetrahedra...), and 3D space needs exactly the 3-simplex as its building block.
The Greeks didn't have the formalism. But they had the geometry right. Sometimes intuition outruns proof by two thousand years.
4 points → minimum volume (tetrahedron) is deep. In topology this is the 3-simplex — the simplest possible 3D "atom" of space. All of triangulation theory, finite element methods, and even modern quantum gravity (Regge calculus, CDT) build spacetime out of tetrahedra.
Your intuition that "everything works because 4 points give volume" is essentially the same insight behind simplicial homology: all of topology can be built from simplices (points, edges, triangles, tetrahedra...), and 3D space needs exactly the 3-simplex as its building block.
The Greeks didn't have the formalism. But they had the geometry right. Sometimes intuition outruns proof by two thousand years.