Rath's (1873 -1874) construction of Pythagorean Triples
- Johannes Boot
It is well known that all Pythagorean triples can be generated from two positive integers m and n. Iff n<m, m and n relatively prime and not both odd, the three numbers a=m²-n², b=2mn, and c=m²+n² form a primitive Pythagorean triple. Rath (1873-1874) has taken the difference between m and n to be equal to d. Use the sliders to change the values of n and d. Note that the product of n and d is equal to the radius of the incircle (r=nd).
Rath H, Die rationalen Dreiecke, Archiv der Mathematik und Physik. v.55-56.1873-1874