mathematical idealization of the trace left by a moving point

A curve is a line that turns or bends. A curved line is never straight, and a curved surface is a surface that is never flat. Some curves can be drawn on paper, but some curves, like a helix, can only be seen in 3-D. A circle is a curve that can be described with the formula x2 + y2 = r2. x and y are used as in a Cartesian coordinate system, and r is the radius of the circle (distance from the center to the outside). Many other curves can also be described with a formula like that.

This is a line that curves.