Curve

A smoothly-flowing path (no sharp changes).

In common language a curve bends (changes direction).

In Mathematics a curve is a continuous, smoothly-flowing path in space. It can be thought of as the path traced by a moving point.

• A curve does not need to bend, a straight line is a special case of a curve
• A curve can be one-dimensional (like a line or a circle) or exist in higher dimensions

Examples of curves: lines, circles, parabolas, sine waves, etc.

When we zoom in closely on any small part of a smooth curve, it resembles a straight line: