Analysis of the Two-Fraction Method for Generating Primitive Pythagoras Triples

Finding methods for generating Pythagorean triples have been of great interest to Mathematicians since the Babylonians (from 1900 to 1600 BC). One of these methods is the less known two-fraction method which works for any two fractions whose product is 2. In this work, we analyse the method and show that it can be obtained from the fact that the excess of a right-angled triangle is even. Using this property, we develop several formulae for generating Primitive Pythagorean Triples. (Contains 4 tables.)