Explain why the phrase "on a plane" is included in the definition of a circle. What would be defined if the phrase were not included?

Question

asnaseer · Answer

you could have a circle on various curved surfaces. "on a plane" isolates the problem to a flat plane.

anonymous · Answer

consisting of those points (in a plane) that are a given distance from a given point

without in a plane , it would be sphere

chriss · Answer

Well a circle is a two dimensional object and thus would always live on a plane which is also two dimensional in nature.  By using the phrase however, you allow for circles that live on planes that don't necessarily inhabit the x-y plane.  in the real world, planes just like lines can be defined in any direction including directions that move them above, below, to the right or left or even across the x-y or y-z planes.