Question

Classify the following curve as open or closed:

Answer 1

Hint:Now if there are gaps in the curve then we will say the curve is open. If the curve is closed then there will be no gaps in its sides. Hence we will use this knowledge to judge if the curve is open or closed.

Complete step by step answer:
Now first let us understand geometrical figures.
Now anything that we can draw on paper can be called a figure. Though in mathematics we name some of the common figures that we see in everyday life. In mathematics, we study such figures to understand them more. Now for example consider a TV. The shape of TV is called a rectangle.
The shape rectangle looks like this

Now consider the shape of a dish.
This shape is called circle.
And this shape looks like.

Now consider the structure given below.

This structure is called an arc.
Now consider all the shapes we mentioned above except arc.
We see that the structures have no gaps in between. Basically the edges or sides are closed curves. These are called closed structures.
But things are different with arc. Arc is just one part of circle. And there is a huge gap too. These structures are called open curves
Now for clarity let us take one more example.

Now even in this structure we can see a gap, hence it is an open structure.
Now consider the given curve.

We can say that the curve has no gaps and is completely closed. Hence we say the curve is a closed curve.
Note:
Now when we draw a closed curve we can reach the starting point of the curve without lifting the pencil and changing the structure. Hence if you can draw a curve in this manner then the curve is a closed curve. Else it is an open curve.