Editing Barycentric coordinate system (section)

==Relationship with Cartesian or affine coordinates==
Barycentric coordinates are strongly related to [[Cartesian coordinates]] and, more generally, [[affine coordinates]]. For a space of dimension {{mvar|n}}, these coordinate systems are defined relative to a point {{mvar|O}}, the [[origin (mathematics)|origin]], whose coordinates are zero, and {{mvar|n}} points <math>A_1, \ldots, A_n,</math> whose coordinates are zero except that of index {{mvar|i}} that equals one.

A point has coordinates 
<math display=block>(x_1, \ldots, x_n)</math> 
for such a coordinate system if and only if its normalized barycentric coordinates are
<math display=block>(1-x_1-\cdots - x_n,x_1, \ldots, x_n)</math>
relatively to the points <math>O, A_1, \ldots, A_n.</math>

The main advantage of barycentric coordinate systems is to be symmetric with respect to the {{math|''n'' + 1}} defining points. They are therefore often useful for studying properties that are symmetric with respect to {{math|''n'' + 1}} points. On the other hand, distances and angles are difficult to express in general barycentric coordinate systems, and when they are involved, it is generally simpler to use a Cartesian coordinate system.