Synonym for centre of gravity or the centre of a plane figure.

In this figure, point G, the meeting point of the medians of triangle ABC, is the centroid of the triangle. If this triangle were placed on the tip of a pencil at point G, it would be perfectly balanced

Etymological Note

The barycentre (from the Greek βαροσ (baros) meaning “heavy”), a synonym in geometry for centroid,  is the centre of the distribution of the weight or mass of an object.

Educational Note

The term “centroid” is used in various areas of mathematics, including analytic geometry, Euclidean geometry and affine geometry, to indicate the mean (average) position of all the points in a given shape. This concept is also applied in physics, astronomy and solid mechanics.

We sometimes use the term “balance point” to refer to the centroid of several points that have the same magnitude or weight. Therefore, the balance point of two points on the geometric plane is the midpoint of the segment joining the two points. The balance point of a triplet of points is the intersection point of the medians of the triangles whose vertices are the three points.

To find the centre of a convex or non-convex polygon, we commonly use its centre of gravity—or centroid—which can sometimes be found using geometric methods, as is the case, for example, with a triangle (in which the centroid is the intersection point of its medians), a parallelogram (in which the centroid is the intersection point of its diagonals) and a regular polygon (in which the centroid is the centre of the circumscribed circle of the polygon).

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