Calculation of the center of gravity of a polygon

That is to say A_1A_2A_3 {\ cdots} A_n a Polygon. Its center of gravity G is given by the following vectorial relation:

\ vec {A_1G} = \ frac {1} {N} \ sum_ {i=1} ^n \ vec {A_1A_i}

It is about a particular case of Barycentre.

The center of gravity of a triangle is at the point of contest Médiane S. It is to the 2/3 the length of each median, more far from the top that medium of the opposite edge.

The center of gravity of a Parallélogramme is the medium of the diagonals.

Regular polygon

If the polygon is regular, its center of gravity is also center of the circles inscribed and circumscribed to the polygon. If the polygon has an even number on sides, the center of gravity is in the middle of the segments uniting a side at the opposite side; it is center of symmetry for the polygon.

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