64=65 Geometry Paradox
This is some funny math. It’s known as the “64 = 65 Geometry Paradox.” Does it make sense to you? (It didn’t to me either.) I’ve since researched it and learned an illusion arises from the fact that the edges of the four pieces, which lie along the diagonal of the formed rectangle, do not coincide exactly in direction. This diagonal is not a straight segment line but a small lozenge (diamond-shaped figure), whose acute angle is arctan 2/3 – arctan 3/8 = arctan 1/46 which is less than 1 degree 15′. Only a very precise drawing can enable us to distinguish such a small angle. Using analytic geometry or trigonometry, we can prove that the area of the “hidden” lozenge is equal to that of a small square of the chessboard. (So I’m told.)
… did you get all that? (I had to read it twice, too.) A shout out to all you smart mathematicians for understanding this “stuff” and making my head spin!
