Patterns of Squares Around an Arbitrary Triangle

H. Ebisui and J.C.G. Notrott studied patterns of squares around respectively a right and an arbitrary triangle, thus generalizing the Pythagorean theorem. We construct a new pattern of squares around an arbitrary triangle, based on the four squares theorem, using simple vector constructions to avoid trigonometric calculations. This gives rise to some known number sequences, with new applications on a geometric pattern of squares.