(February 23, 2022 at 5:12 pm)highdimensionman Wrote:(February 23, 2022 at 10:34 am)polymath257 Wrote: And we similarly define a sphere in three dimensions the same way. The same definition even works in any metric space, although there are some counter-intuitive situations in that generality.
There is a another curved shape that follows as a set of all points that are equidistant from a given point. Unfortunately I can't remember what the geometry was called and can't find it anywhere now. I'll keep looking though.
Do you mean another shape in 2d realm besides the circle? I fail to see what that could be.