Curve – Definition with Examples

What is Curve?

A curve is a continuous and smooth flowing line without any sharp turns. One way to recognize a curve is that it bends and changes its direction at least once.

Types of Curves

   1. Upward curve: A curve that turns in the upward direction is called an upward curve.  It is also known as a concave upward. Concave Upward also called or “Convex Downward

upward curves

   2. Downward curve: A curve that turns in the downward direction is called a downward curve. It is also known as a concave downward. Concave Downward also called or “Convex Upward”.

downward curves

   3. Open curve: An open curve does not enclose any area within itself and it has two endpoints.  Some of the open curves are given in the figure below.

open curves

   4. Closed curve: A closed curve, has no end points and encloses an area (or a region). It is formed by joining the end points of an open curve together.

      Circles , ellipses are formed from closed curves. 

closed curves

   5. Simple Curve: A simple curve changes direction but does not cross itself while changing direction. A simple curve can be open and closed both.

closed simple curve and open simple curve

   6. Non-simple curves: A curve that crosses its own path is called a non-simple curve. 

non simple open curve and non simple closed curve

Curves around us

  • Race track: A race The track from the figure looks like a closed curve. 
  • Roads: Roads on hills and mountains are curvy.
Real life examples of curve
Fun Facts
– A curve is made up of many small line segments joined from end to end.  If you look at a curve very closely, you will see the lines.