Introduction to Classical Mechanics · Problem 11.51
Relativity (Kinematics) — Morin
Physics — Mechanics · pythagorean-triples
Problem
Let (a,b,h) be a Pythagorean triple. (We'll use h to denote the hypotenuse, instead of c, for obvious reasons.) Consider the relativistic addition or subtraction of the two speeds, β1=a/h and β2=b/h. Show that the numerator and denominator of the result are the leg and hypotenuse of another Pythagorean triple, and find the other leg. What is the associated γ factor?