## Generating scalene Heron triangles — Part 1

One can generate scalene Heron triangles by finding two different Pythagorean triangles that share one common side.

That means, we need to find four odd numbers.

we can use these formulas to generate Pythagorean triangles

$a \; = \; (m^2 - n^2) \,/ \,2$
$b \; = \; m \, n$
$c \; = \; (m^2 + n^2) \,/ \,2$

$((m^2 - n^2) \,/ \,2)^2 \; + \; (m \, n)^2 \; = \; ((m^2 + n^2) \,/ \,2)^2$

we can create another Pythagorean triangle with the formula

$d \; = \; (p^2 - q^2) \,/ \,2$
$e \; = \; p \, q$
$f \; = \; (p^2 + q^2) \,/ \,2$

In order to find four odd numbers, one must find an odd number made up of the product
of three odd numbers, in which two of the numbers must be different.

$m \, n = p \, q$

See the table below:

Here are all the triangles for   $\, b < \, 500$