Dissections 1+2=√5 of polygons
Here we consider the problem (proposed by Livio Zucca) to dissect a monomino (or a domino or a triomino or a tetromino) of side 1 and its double in the smallest number of pieces that can be rearranged to form a similar figure sqrt(5) times larger (since 1+4=5). For the same dissection problem with other shapes see here.
If you know find better solution, let me know. (Drawings by Livio Zucca).