Question

What is a non-polygon?

Answer 1

Hint: A non-polygon can be defined as that geometric object that does not conform to the definition of a polygon. To get a better idea of what a non-polygon is, we should first know what a polygon is. A polygon can be defined as any geometric object that consists of a finite number of line segments and satisfies certain conditions.

Complete step by step solution:
The conditions a polygon satisfies is,
Let the finite number of line segments be labelled as ${{s}_{1}},{{s}_{2}},{{s}_{3}}.....{{s}_{n}}$. Now, the conditions that the polygon must satisfy are as follows:
1. The line segments in a polygon are all connected sequentially and form a closed figure. This can also be stated as the end of ${{s}_{1}}$ will coincide with the beginning of ${{s}_{2}}$, end of the segment ${{s}_{2}}$ will coincide with the beginning of the segment ${{s}_{3}}$ and so on. This will continue till the end of ${{s}_{n}}$ coincides with the beginning of ${{s}_{1}}$.
2. All the points of coincidence of the finite number of segments in the polygon are different. No, two points of coincidence overlap with each other. All the coincidence points are distinct and different from each other.
3. Except from the points of coincidences, there are no other intersection or coincidence points among the finite number of segments.
These are the properties that define a polygon and if the figure satisfies all these three properties then it is called a polygon.
Now, we can say that a geometric object that does not satisfy one or more of the above mentioned properties or conditions can be said to be a non-polygon.
Hence, a non-polygon can be defined as a geometric figure or object that satisfies the definition of a polygon.

Note: A polygon can also be defined as a two-dimensional and planar figure or object and has straight lines as segments. Therefore, shapes that include an arc are not polygon. This implies that a circle or an oval are not polygons.