It can be shown that all Pythagorean triples can be obtained, with appropriate rescaling, from the basic Platonic sequence ("a", and ) by allowing "a" to take non-integer rational values. If "a" is replaced with the fraction "m"/"n" in the sequence, the result is equal to the 'standard' triple generator (2"mn", ,) after rescaling. It follows that every triple has a corresponding rational "a" value which can be used to generate a similar triangle (one with the same three angles and with sides in the same proportions as the original). For example, the Platonic equivalent of (56, 33, 65) is generated by "a" = "m"/"n" = 7/4 as ("a", ("a"2 –1)/2, ("a"2+1)/2) = (56/32, 33/32, 65/32). The Platonic sequence itself can be derived by following the steps for 'splitting the square' described in Diophantus II.VIII.