PAIRS OF PYTHAGOREAN TRIANGLES WITH GIVEN RATIOS BETWEEN CATHETI

摘要

We investigate the problem of finding pairs of Pythagorean triangles (a, b, c), (A, B, C), with given cathetus ratios A/a, B/b. In particular, we prove that there are infinitely many essentially different (non-similar) pairs of Pythagorean triangles (a, b, c), (A, B, C) satisfying given proportions, provided that Aa not equal Bb.