The Online Encyclopedia of Integer Sequences has a search facility, so that if you have a mysterious sequence of integers you can put it in any see whether it's

The Online Encyclopedia of Integer Sequences has a search facility, so that if you have a mysterious sequence of integers you can put it in any see whether it's one of the sequences in the OEIS (or do fancier things -- see whether it's a subsequence of one of those sequences, enter just one large number from the sequence to see whether other seqs containing that number are enlightening, etc.). The obvious counterpart for this (I think) would be to have a set of "standard" triangles, including a couple with random vertex positions that hopefully satisfy no "interesting" mathematical relationships, and report (say) 12 decimal places of the coordinates of each centre for each of those triangles. Then, if you run across some mysterious point in a triangle, you can look for its coordinates and see whether they match any of the centres. (This would also give a way of verifying that no two of the thousands of triangle centres catalogued here are coincidentally equivalent to one another.)