Henry Dudeney gives a method for dissecting a square so that its pieces can be rearranged to form a pentagon. I found it in a copy of Dudeney’s book “Amusements in Mathematics” on Project Guetnberg here. It is puzzle #155 (“Pentagon and Square”) and I found another copy of it here:
You will notice that two points are labeled ‘F’, one inside the pentagon and one inside the square. I’m embarrassed to say it took me a good fifteen minutes to sort this out but the one inside the square should be labeled ‘E’. I am further embarrassed to say I didn’t know what “mean proportional” meant in his instructions. Uncle Google to the rescue!