Is there some paper or do you know how to show that the 3 typical definitions for barycentric coordinates are equivalent?
I only found papers stating these definitions, not proofing their equivalence. One such paper stating these definitions (p. 1-2) can be found here: https://bmos.ukmt.org.uk/home/areals.pdf
(It says there is some proof of the equivalence of these 3 definitions left in the appendix, however I cannot find one there...)