[cshimmin]

Well, technically a circle can't be said to be a function but not for the reason you mean. A circle is a collection or a set of points, for example in a 2d plane, that are equidistant from a center point.

Probably what you are trying to say is that "a circle is not the image of a function", but that is also not true. You're assuming since in cartesian coordinates you can solve for y = +/- sqrt(R^2 - x^2), the fact that y is multi-valued means it's not a function. This is what they teach in highschool pre-calculus anyway.

But for example, we can associate the points on a circle with the image of the function e^{i theta}. Or equivalently, with the R^2-valued function f(theta) = (cos(theta), sin(theta)).