Subj:     A Chessboard Paradox (S460)
          From: Jigsaw Paradox on 11/12/2005
          (See 'Two triangles Problem' in ILLUSIONS)

Source:
http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/jigsaw-paradox.html

Take the chess on the left and cut it along the lines shown.  Use the four parts to form the rectangle on the right.  The square on the left has an area of 64 squares while the rectangle on the right has an area of 65 squares.  How is this possible?
 

Sam Loyd presented this fallacy to the first American Chess congress 1858. The first time this was seen in print was (1868), a "Kurze Mitteilung" of the Editor O. Schlömilch. Eleven years later (1879) Schlegel published the Fibonacci generalization