Take a pencil and a paper. Put the tip of the pencil on the paper and without lifting it move it aimlessly from one point to the other. The figure so obtained can be in any one of the shapes.
Such figures are called curves. Similarly, if we take a piece of paper and it is just doodled.Then the pictures obtained as a result of doodling are called curves.
In our day-to-day life the word ‘curve’ means ‘not straight’. However, in Mathematics a curve can be straight as shown.
A curve which does not cut itself is called an open curve.
are open curves.
A curve which cuts itself is called a closed curve.
are closed curves.
Position of a point with respect to a Curve:
If a closed curve is drawn on the plane of the paper, then it divides the plane into three disjoint parts:
1) The points lying inside the curve or the interior of the curve.
2) The points lying on the curve or the boundary of the curve.
3) The points lying outside the curve or the exterior of the curve.
The interior of a curve together with it’s boundary is called its region.