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There can be any number of points on a plane, or even on a line - and any number of lines on a plane.
A minimum of three points are required to define a plne (if they are not collinear). And in projective geometry you can have a plane with only 3 points. Boring, but true. In normal circumstances, a plane will have infinitely many points. Not only that, there are infinitely many in the tiniest portion of the plane.
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Two. Two points determine a line. Three points determine a plane.
There can be any number of points on a plane, or even on a line - and any number of lines on a plane.
A plane has an infinite number of points. It takes 3 points to fix a plane i.e. you need 3 points to identify one unique plane.
A minimum of three points are required to define a plne (if they are not collinear). And in projective geometry you can have a plane with only 3 points. Boring, but true. In normal circumstances, a plane will have infinitely many points. Not only that, there are infinitely many in the tiniest portion of the plane.
If you are given a plane, you can always find and number of points that are not in that plane but, given anythree points there is always at least one plane that goes through all three.
They are points on a coordinate plane.
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the triangular distribution of points on a plane is the minimum energy limit of randomly seeded points on a plane - it is as far apart as they can get. the voronoi tesselation of equally spaced triangular points is hexagonal, the minimum energy network that tesslates the plane. you can develop susch tesselations using reaction diffusion models. adamatsky shows some in his 2001 book