Pythagorean Triads

Abstract

The object of this report is to examine algorithms for generating pythagorean triads: triplets [a,b,c] of positive integers such that the pythagorean relation a squared + b squared = c squared is satisfied. Such triplets can be interpreted, of course, as examples of right angled triangles with integer sides and are therefore constructable by the methods of euclidean geometry (compass and ruler). The best known such triplet is [3,4,5] which is also the smallest. Every schoolchild must be familiar with [3,4,5] in constructed trigonometric exercises; possibly also with [5,12,13] which is also frequently met in such circumstances. NOTE: This deposit is an OCR conversion of a 1975 report and hence may contain some errors, though care has been taken with proofreading.