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Hmm. Why only 2? Why not 3 points? Can you find an interesting curve produced by a constant product of distances from N points? Maybe even in higher dimensions,
by slippy 2y ago
Hmm. Why only 2? Why not 3 points? Can you find an interesting curve produced by a constant product of distances from N points? Maybe even in higher dimensions, for 1 point, you have a sphere. What is the shape for 2 points? Is it more like an hourglass-like double droplet?
- amelius 2y agoThere is a generalization: > Back before Twitter became a Nazi bar, I issued a challenge there: find a whole series of numbers like pi, each with its own bunch of formulas. @duetosymmetry took me up on this and invented the numbers ϖₙ: (...)
- plank 2y agoYes. But the question remains: is there a geometrical analogue?
- knappa 2y agoOn the 3 points bit: One and two points are special. In each of these cases, there is, up to translations and uniform scaling, only one configuration. When you have three points, though, there are as many configurations as there are similar triangles. You could probably get a number for each similarity class of triangle, but you shouldn't expect to get a constant across all classes.