A Historically Motivated Study of Families of Pythagorean or Babylonian Triples and Their Generating Semigroups of p- or B-Orthonormal Matrices

摘要

The role played by the triple S,T,V of basic generator matrices of the Lorentz orthonormal 3 X 3 matrices in Pythagorean triples generation was studied as well as the characteristic properties of the matrices S,T,V themselves and their positive powers. The approach used is to work simultaneously with the Pythagorean triples and their parameter pairs, related to each other by a well known parametrization formula. Several problems known since ancient history are recalled and analyzed, including the Babylonian triples known as solutions of certain trapezoid partition problems.