What is a non-polygon?

1 Answer
Zor Shekhtman ยท EZ as pi
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.

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