3 ms·
I mean the concept of distance from 3 points introduces a mess of metrics or even measure theory. 2 points always have a shortest path between each other, so t
by VHRanger 2y ago
I mean the concept of distance from 3 points introduces a mess of metrics or even measure theory.
2 points always have a shortest path between each other, so the constant is about this fact. For 3 points you have the whole universe of possible triangle shapes to contend with.
- jovial_cavalier 2y agoIt's easy to generalize this to more points. https://www.desmos.com/calculator/fo7tqlfjgo https://www.desmos.com/calculator/fo7tqlfjgo
- vitus 2y agoShortest path between two points still depends on your metric. For instance, if you're constrained to travel along the surface of Earth, your shortest path is going to travel along a great circle, rather than pass through the interior of the sphere. That said, you could, for instance, pick the three vertices of an equilateral triangle (using the Euclidean distance as your metric of choice, as we do in order to derive the lemniscate and the circle), and again deal with the product of the distances from each vertex. You again start with small circles around each vertex, which eventually expand to a single looping curve, and then into ovals encircling the entire triangle. https://en.wikipedia.org/wiki/Cassini_oval#Generalizations https://en.wikipedia.org/wiki/Cassini_oval#Generalizations https://en.wikipedia.org/wiki/Polynomial_lemniscate#Erd%C5%91s_lemniscate https://en.wikipedia.org/wiki/Polynomial_lemniscate#Erd%C5%9...