I’ve spent 10 minutes googling things like “triangular coordinates“ and “reduced barycentric coordinates“ but haven’t found what I’m looking for. So, apologies if you feel I should have googled longer instead of wasting funsters’ time, but maybe one of you will instantly know the name of the coordinate system in which points in the plane are represented by triples summing to zero (and more generally n-tuples summing to zero in higher dimensions). Actually, I might as well include a followup question, which is, where is the best place to look for translations of the standard high school formulas for coordinate geometry into this somewhat arcane coordinate system? I could spend an hour figuring them out for myself, but that’s an hour I’d rather spend figuring out something new, and more importantly, I might make mistakes! Thanks, Jim Propp