New relationships between Pythagorean Triples: Composition and Decomposition of triples

Ancient Babylonians used Pythagorean triples to conduct real-life calculations but, although that was nearly 4000 years ago, these triples have not been greatly studied. This article helps to rectify this, by proposing six Composition Laws and six Decompostion Laws by which any two Pythagorean triples can be composed and decomposed to generate and arise from all other triples.