Integer triangle formula_112 and formula_113 generate the same triple. Unfortunately the two pairs can both be of gcd=3, so we can't avoid duplicates by simply skipping that case. Instead, duplicates can be avoided by formula_27 going only till formula_115. Note that we still need to divide by 3 if gcd=3. The only solution for formula_116 under the above constraints is formula_117 for formula_118. With this additional formula_119 constraint all triples can be generated uniquely. An Eisenstein triple is a set of integers which are the lengths of the sides of a triangle where one of the angles is 60 degrees. Integer triangles
Angle bisector theorem of the length of side "AB" to the length of side "AC": and conversely, if a point "D" on the side "BC" of triangle "ABC" divides "BC" in the same ratio as the sides "AB" and "AC", then "AD" is the angle bisector of angle "∠ A". The generalized angle bisector theorem states that if "D" lies on the line "BC", then Angles "∠ BAD" and "∠ DAC" are equal. Therefore, the right hand sides of equations () and () are equal, so their left hand sides must also be equal. which is the angle bisector theorem. If angles "∠