# barycentric coordinates

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## barycentric coordinates

(ba-ră-**sen**-trik) See barycenter.

## Barycentric Coordinates

the coordinates of a point *M* on a plane in relation to three basis points *A*_{1}, *A*_{2}, and *A*_{3} (not lying on the same line) of this plane—three numbers *m*_{1}, *m*_{2}, and *m*_{3} (which satisfy the condition *m*_{1} + *m*_{2} + *m*_{3} = 1), such that the point *M* represents the center of gravity of the system of three material points with masses *m*_{1}, *m*_{2}, and *m*_{3} located at the points *A*_{1}, *A*_{2}, and *A*_{3} respectively. (Here it is necessary to consider that the masses *m*_{1}, *m*_{2}, and *m*_{3} can be both positive and negative.) Barycentric coordinates in space are defined analogously. Barycentric coordinates are used in certain branches of mathematics and its applications.

## barycentric coordinates

[‚bar·ə′sen·trik kō′ȯrd·ən‚əts] (mathematics)

The coefficients in the representation of a point in a simplex as a linear combination of the vertices of the simplex.