Coming across this classic geometric paradox recently in Futility Closet motivated me to write down its solution in detail.
“Where did the empty square come from?”
In any case, this is the canonical example for why I avoid visual geometric proofs—you can be so easily fooled. Real proofs require plane or analytic geometry arguments.
See the Classic Geometry Paradox
(Update 9/14/2024) Penn & Teller – Fool Us – Magic Trick
I just saw a rerun of a Penn & Teller – Fool Us episode (Season 10 Episode 17) in which they performed a magic trick (@45:30) that amazingly used a version of this classic geometric paradox.