3 ms·
This is not even close. Obviously you missed a crossed circle and every tesselation of regular polygon has at least one of those. And that's just a start. Metr
by AstralStorm 7y ago
This is not even close.
Obviously you missed a crossed circle and every tesselation of regular polygon has at least one of those. And that's just a start.
Metric spaces are a huge area of mathematics.
1) Question did not mention distinct points. Two joined equal length segments with overlapping points qualify.
2) Question did not mention metric used, you assumed euclidean distance.
3) There are many more solutions in multidimensional spaces even just for euclidean metric. Question did not specify 2D euclidean (but explanation sort of assumed that) nor even planar. Have fun finding these in hyperbolic geometry - current model of reality due to General Relativity. Or in quantized space.
4) Do infinite distances count as distinct? Zero distances are more obvious, but what about zero limits with different signs?
Mainly etc. Never ask a general question about geometry. ;)
- kangnkodos 7y agoI deleted my list of spoiler solutions. But you are correct. I was only thinking in 2D euclidean space. Khaaaaaan! Your other ideas are very creative, and as far as I understand them, correct (except for the idea of four DISTINCT points), but probably outside the problem. How many solutions would there be on a hyperbolic plane? No idea.
- sonofgod 7y ago1) is answered in the article Clarifications: The four points must be distinct. That is, no point is allowed to be superimposed on another point.