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I thought I would share with our chess-loving readers the following interesting (and somewhat well-known) mathematical chess paradox , apparently proving that $64=65$, and the accompanying explanation offered by Prof. Christian Hesse, University of Stuttgart (Germany).  It shows a curious connection between the well-known Cassini’s identity (related to Fibonacci numbers) and the $8 \times 8$ chessboard ($8$ being a Fibonacci number!). The connection can be exploited further to come up with similar paradoxes wherein any $F_n \times F_n$ -square can always be “rerranged” to form a $F_{n-1} \times F_{n+1}$ -rectangle such that the difference between their areas is either $+1$ or $-1$. Of course, for the curious reader there are plenty of such dissection problems listed in Prof David Eppstein’s Dissection page.

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