The difference between Barycentre and Centroid
When used as nouns, barycentre means the point at the centre of a system, whereas centroid means the point at the centre of any shape, sometimes called centre of area or centre of volume. for a triangle, the centroid is the point at which the medians intersect. the co-ordinates of the centroid are the average (arithmetic mean) of the co-ordinates of all the points of the shape. for a shape of uniform density, the centroid coincides with the centre of mass which is also the centre of gravity in a uniform gravitational field.
check bellow for the other definitions of Barycentre and Centroid
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Barycentre as a noun (mathematics, physics, astronomy):
The point at the centre of a system; an average point, weighted according to mass or other attribute. The term is usually used in astronomy for the centre of mass about which a system rotates, for example, the moon and the earth rotate about a common point within the earth but not near the centre. Jupiter and the Sun rotate about a common point just outside the surface of the Sun.
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Centroid as a noun (mathematics, physics):
The point at the centre of any shape, sometimes called centre of area or centre of volume. For a triangle, the centroid is the point at which the medians intersect. The co-ordinates of the centroid are the average (arithmetic mean) of the co-ordinates of all the points of the shape. For a shape of uniform density, the centroid coincides with the centre of mass which is also the centre of gravity in a uniform gravitational field.