In my last post I presented a paradox, where a set of four pieces forming an 8×8 square could apparently be rearranged to form a 5×13 rectangle, summoning an extra unit of area out of thin air.
Quite a few commenters realized that the pieces don’t actually quite fit together in the second figure, leaving a small gap which is covered up by the thick black lines (that, or else the second figure uses slightly differently-shaped pieces!). Here are the figures again, this time without the thick lines:
That thin white area in the middle has an area of—you guessed it—one square unit.
In a subsequent post I’ll explain why this works so well. As noted by JM, it’s not a coincidence that all the dimensions involved are Fibonacci numbers…