# What is a non-polygon?

Dec 25, 2015

Non-polygon is a geometric object that does not conform the definition of polygon (see below).

#### Explanation:

Polygon is a geometric object that consists of certain finite number of segments (let's label them ${s}_{1}$, ${s}_{2}$,..., ${s}_{N}$) that satisfy the following conditions:

(a) they are sequentially connected into a closed figure, that is the end of ${s}_{1}$ coincides with the beginning of ${s}_{2}$, end of ${s}_{2}$ coincides with beginning of ${s}_{3}$ etc... end of ${s}_{N - 1}$ coincides with beginning of ${s}_{N}$ and end of ${s}_{N}$ coincides with beginning of ${s}_{1}$;

(b) all the points of coincidence mentioned above are different;

(c) there are no other intersection points among these segments.

In addition: Note that polygons are two-dimensional, (planar) and that the segments are straight lines, so any shape which includes an arc is not a polygon. (A circle is therefore not a polygon).

A geometric object that does not satisfy one or more of these three conditions IS NOT a polygon and you can name it a non-polygon.