What’s the aspect ratio of a rectangle such that dividing it in half, perpendicular to its longest side, yields two smaller rectangles of the same aspect ratio?

 w/h = h/(w/2)
w²/2 = h²
  w² = 2h²
   w = h√2
 w/h = √2 ≈ 1.414

Which is curiously (or conveniently) in between the 4/3 aspect ratio of point and shoot cameras and the 3/2 aspect ratio of 35mm cameras, described in On aspect ratios and photography.