Changes

Example: When ''n'' = 2, the triple produced is 5, 12, and 13.

Example: When ''n'' = 2, the triple produced is 5, 12, and 13.

(This formula is actually the same as method I, substituting ''m'' with 2''n'' + 1.)

(This formula is actually the same as Euclid's method, substituting ''m'' with 2''n'' + 1.)

Alternatively, one can generate triples from even integers using the following formulas.  Given that ''m'' is an positive even number,

Alternatively, one can generate triples from even integers using the following formulas.  Given that ''m'' is an positive even number,

Example: When ''m'' = 4 the triple produced is 8, 15, and 17

Example: When ''m'' = 4 the triple produced is 8, 15, and 17

(This formula is another specific case of method I, substituting ''n'' with 1).

(This formula is another specific case of Euclid's method, substituting ''n'' with 1).

If one creates a scatter plot of Pythagorean triples, then patterns emerge in the form of parabolas of point densities. Albert Fässler and others provide insights into the significance of these parabolas in the context of conformal mappings.<ref>[http://conservancy.umn.edu/handle/4878 1988 Preprint] See Figure 2 on page 3., later published as  

If one creates a scatter plot of Pythagorean triples, then patterns emerge in the form of parabolas of point densities. Albert Fässler and others provide insights into the significance of these parabolas in the context of conformal mappings.<ref>[http://conservancy.umn.edu/handle/4878 1988 Preprint] See Figure 2 on page 3., later published as