For a GP 1, r, r^2 to form the side lengths of a triangle when r>1

the following inequalities must be satisfied:-

r^2-1<r and r^2+1>r. This means that r must lie in the range

1<r<phi where phi is the Golden Ratio.

However when r<1 then the equalities are:-

1-r^2<r and r^2+1>r. This means that r must lie in the range

1/phi<r<1.

Consequently for any GP to form the sides of a triangle, its common ratio r

must lie in the range:-

1/phi<r<phi.

Apart from articles on Kepler's Triangle, the special case where

r=sqrt(phi), I am unable

to find any references to the generalised case and the valid range for r.

There must be some references on this subject, Can anyone help?

Thanks

Frank Jackson