Barycentric Coordinates

Where is the center of gravity of a discrete set of masses? Möbius observed in 1827 that this elementary computation goes beyond its mere use for engineering, for the masses themselves can be used as coordinates that replace “parallel coordinates” [70]. His new coordinate system, which he dubbed barycentric or weight-centric, was, as mentioned at the start of Chapter 12, one instance of four near-simultaneous discoveries of homogeneous coordinates.

Readers who wish to pursue the original manuscripts will find pointers to translations of many fundamental works in Grattan-Guinness’s recent volume [43] (though, strangely,Möbius’ work is omitted; even more strangely, his Barycentric calculus appears to have never been translated). After encountering ideal points, or points at infinity, in Chapters 11 and 12 through projection, we encounter them once again in this chapter through algebraic manipulation.