Triangles with sides in a GP
- Dear All
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
Consequently for any GP to form the sides of a triangle, its common ratio r
must lie in the range:-
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?