Question

Is there a more general name for the curve that an ellipse and circle fall into, i.e. something that, if a parametrized function, "completes" itself by circling back to its original point within a cycle and endlessly following that same path?

Answer 1

Only thing I can think of is an ellipsoid that extends in one axis. The cross sections are circles. Don't know if that is what you're looking for lol. x^{2] + y^{2} + z^{2} = 1

Answer 2

The special case I wrote is a sphere. But It can also be x^2 / 9 + y^2/9 + z^2 = 1

Answer 3

I'm looking for a general *name* encompassing both ellipses and spheres, unless it's just "ellipse", because a sphere is a special case of an ellipse, and an ellipse a special case of an ellipsoid. I'm not finding a satisfactory answer, so I think I'll drop it for the time being.

Answer 4

(Nonetheless, thank you.)

Answer 5

A sphere isn't a special case of an ellipse. An ellipse is a 2D shape, a sphere and an ellipsoid are 3D objects.

Answer 6

As I said an ellipsoid as a shape of an ellipse in 2 dimensions. When extended in the remaining axis, the cross sections are circles.

Answer 7

*WHOOPS*, didn't mean to say sphere, at all. That was a typo.

Answer 8

But again, I'm just looking for-if it exists-a general name for ellipses and circles, and those only; If I say "special cases of ellipsoids", I am including all variants. I'm wondering if there's a name that encompasses just ellipses, and just circles, where that's a little redundant due to a circle being a special case of an ellipse, and I'm guessing I should conclude that the general term is "ellipse", but again, that's kind of unsatisfactory.

Answer 9

Or, correction, "special cases of ellipsoids" is kind of clunky. I'm wondering if there is a single word, one term, no "special cases" to describe circles and ellipses, and I'm guessing that that's just "ellipse".

Answer 10

Yeah, I would say a circle is a special case of an ellipse. Don't know a term that can encompass both I suppose.