Show that every pythagorean triple obtained using the Platos

Show that every pythagorean triple obtained using the Plato\'s formula can be obtained using the babyloanian formula. (Write the variables m,n of the babyloanian formula in terms of the variable r of the Platos formula). Plato\'s: If s is an integer with s>2 then a=2s, b=s²-1, c=s²+1

Solution

The plato\'s triple are given by 2m,m²-1 and m²+1.

The babyloanian triples are given as (p²-q²,2pq,p²+q²⁾

^taking q² Conon from the series, the triple can be written as

((p/q) ²-1,p/q,(p/q)²+1).

This is a plato\'s formula expression.