Dissection of a rectangle into rectangles with given side ratios
  Given a collection of N rectangles such that the side ratio of each one is a quadratic irrationality, we find all rectangles which can be tiled by rectangles similar to one of the given ones. It means that each possible shape can be used several times or not used at all, so that the number of rectangles in the tiling is not necessarily equal to N. 
Fyodor Sharov
math.CO