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