In article <firstname.lastname@example.org>, email@example.com wrote:
> >What about the set of all points on a perfect circle (ie all solutions to > >x^2 + y^2 = 1). > > Well technically of course all solutions you point out define a > perfect sphere not a perfect circle.
With only two variables, x and y, there is no need to presume three dimensions, but if one does, one gets a right circular cylinder, not a sphere.
If one doesn't assume three (or more) dimensions, one does get a circle.