To proceed fully into the establishment of the meaning of the term convex polygon, it is necessary, first, to determine the etymological origin of the two words that shape it:
-Polygon derives from the 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, meanwhile, emanates from Latin. It is formed from the prefix "con-", which is equivalent to "together", and from the adjective "vexus", which means "carried."
In the field of geometry , the polygons They are central elements that appear very frequently. This concept refers to flat figures composed of non-aligned straight segments, which are called sides .
The characteristics of the polygons allow them to be classified in different ways. The regular polygons , for example, are those that have internal sides and angles that are congruent to each other. Instead, the irregular polygons Do not share this property.
If we talk about convex polygons , we will refer to the polygons whose diagonals They are always interiors and whose internal angles do not exceed pi radians or 180 degrees.
In addition to all of the above, it is worth knowing other unique data on convex-type polygons:
-All its vertices "point" to what is outside its 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 borne in mind that, in this type of figures, all of its vertices are pointed outwards, that is, outside. On the other hand, if a line is drawn on any side of the polygon, the whole figure will be inside one of the semiplanes that are created by the line in question.
Another way to determine if a polygon is convex is to draw segments between two points on the figure , whatever your location. If these segments are always interior, it will be a convex polygon. If any segment is exterior, or if any of the internal angles exceeds 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 mentioned classifications (also being a regular polygon, to cite a possibility).
Typically, when talking about convex polygons, the term concave polygons 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, so that it can be understood well, the latter are those who have some kind of “entree” 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.