What is convex polygon?

What Does convex polygon Mean

To proceed to fully enter into the establishment of the meaning of the term convex polygon, it is necessary, first of all, to determine the etymological origin of the two words that give it its shape:

-Polygon derives from Greek. Specifically, it is the result of the sum of "poly", which is synonymous with "many", and "gono", which can be translated as "angle".

-Convex, for its part, emanates from Latin. It is formed from the prefix “with”, which is equivalent to “together”, and the adjective “vexus”, which means “carried”.

In the realm of geometry , polygons are central elements that appear very frequently. This concept refers to plane figures made up of non-aligned straight segments, which are called sides .
The characteristics of polygons allow them to be classified in different ways. The regular polygons , for example, are those which have sides and internal angles are congruent. In contrast, irregular polygons do not share this property.

If we talk about convex polygons , we will refer to polygons whose diagonals are always interior and whose internal angles do not exceed pi radians or 180 degrees.
In addition to all the above, it is worth knowing other unique data about convex polygons:

-All their vertices “point” to what is the outside of their perimeter.

-The triangles are all convex polygons.

-In the same way, we must not forget that regular polygons can also be said to be all convex.
There are several ways to find out if a polygon is convex. It must be taken into account that, in this type of figure, all of its vertices are pointed outwards, that is, to the outside. On the other hand, if a line is drawn on any side of the polygon, the entire figure will be inside one of the semi-planes that are created by the line in question.
Another way to determine if a polygon is convex is by drawing segments between two points in the figure , regardless of their location. If these segments are always interior, it will be a convex polygon. If any segment is exterior, or if any of the interior angles exceed 180 degrees, the polygon will be concave.
It should be noted that a polygon can be convex and, in turn, be part of another of the aforementioned classifications (also being a regular polygon, to name one possibility).
The usual thing is that when talking about convex polygons, the term concave polygons also quickly appears. In this sense, it must be said that these are those that have one or more of their angles that are less than 180º. That is to say, so that it can be understood well, the latter are the ones that have some kind of "starter" in what their figure is.

How do you identify a concave one? Taking into account that the segment that joins two interior points of the polygon does not manage to be totally within it.

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