The first thing we are going to do before entering fully into the definition of the term barycenter is to discover its etymological origin. In this case, we can state that it is a word of Greek origin since it is the result of the sum of two components of that origin:
-The noun "baros", which can be translated as "gravity" or "weight".
-The name "kentron", which is synonymous with "sting".
The concept is used in the field of physics to name the center of gravity of something . In the field of geometry , the center of gravity is the point at which the medians that belong to a triangle intersect.
The barycenter of a physical body, when it has a uniform density, is coincident with its center of mass . The same thing happens when matter is distributed in the body symmetrically.
To understand precisely what the center of gravity is, therefore, it is important to know what the ideas of center of gravity and center of mass refer to. The center of gravity is the point of application of the force resulting from the sum of the forces of gravity that affect the different sectors of the body. In a material body, this center of gravity is called the barycenter.
The center of mass, on the other hand, is the geometric point that acts dynamically as if the force resulting from external forces were applied to it. When there is uniformity in density or the material distribution respects certain properties (such as symmetry), the center of mass coincides with the center of gravity (and, therefore, with the barycenter).
For geometry , the center of gravity of the surface that is contained in a plane figure is a point that, with any straight line that passes through it, allows the segment in question to be divided into two parts that have the same moment with respect to this straight line.
In addition to everything stated above, we can indicate these other important aspects:
-The centroid of a segment is the exact center of it.
-The barycenter of a tetrahedron, for example, is the point at which the segments that join each vertex intersect with what is the isobarycenter. We have to explain that this is a center of gravity that stands out for the fact that all the masses are equal to each other.
-If what we want is to know the center of gravity of a triangle we have to state that this will be the intersection of what are the three medians of said geometric figure.
-You must know that when calculating the aforementioned barycenter, the incorporation of what are partial barycenters can be used. That is, by regrouping points.
-On the other hand, it should not be overlooked that the center of gravity will not change if all the masses are multiplied by the same factor.
-A simple and quick way to calculate the center of gravity of a geometric shape is by using a ruler and a compass.