The applet below illustrates a dissection akin to the ones of Curry, Hooper, Langman and Sam Loyd Son. John Sharp mentions it with a reference to his notes in an enlightening article, but demurs as to the source. Originally, a 13×13 square is cut into three pieces which, after a rearrangement appear to combine into an 8×21 rectangle - a loss of one square.
The puzzle is easily modified by changing the dimensions according to the properties of the Fibonacci sequence. Upon rearrangement of the pieces, a single square seems to intermittently appear or disappear.
