Generating new pythagorean triples (triangles)
- 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 are relatively prime and not both odd, the three numbers a=m²-n², b=2mn, and c=m²+n² form a primitive Pythagorean triple (PPT). All PPT's can begenerated from the (3,4,5) triple (m=2,n=1). The three PPT generated by (3,4,5) are (21,20,29), (5,12,13) and (15,8,7). The new PPT's are sometimes called the "children" of the original PPT.
INSTRUCTION:Use the tick boxes to hide or unhide the "children". Change the value of m and n (see new values generated), to generate new (PPT) triples (a,b,c).