Loading ...
Sorry, an error occurred while loading the content.

Triangles with sides in a GP

Expand Messages
  • Frank Jackson
    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. This means that
    Message 1 of 1 , Jul 30, 2010
    • 0 Attachment
      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

      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
    Your message has been successfully submitted and would be delivered to recipients shortly.