# A geometric method to Generate Pythagorean triangles(Barning(1963),Hall(1970))

- Author:
- Johannes Boot

- Topic:
- Triangles

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" or "infants" of the original PPT.

**INSTRUCTION**: Use the tick boxes to display the "children". Change the value of m and n (see new values generated), to generate new triples (a,b,c). Note: The construction is based on the pythagorean ternary tree as developed by Berggren,B (1934), Barning, F J M(1963) and Hall,A (1970).