(February 23, 2022 at 10:34 am)polymath257 Wrote:(February 22, 2022 at 9:27 pm)Fireball Wrote: Yes. In geometry, we define a circle as "the set of all points in a plane that are equidistant from a given point, called the center of the circle". The question posed by the OP shows ignorance of this basic concept.
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.
