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What's wrong with the puzzle in this video?

I didn't understand. Do you understand what happens?

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    $\begingroup$ Just an optical illusion as the "squares" down the middle are not true squares. The sum of the areas of the 4 parts is still 64. $\endgroup$
    – SMS von der Tann
    Aug 9, 2016 at 17:12

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Obviously, $64\neq65$. Observe the diagram below:

enter image description here

The slopes of the diagonals of the blue and pink pieces are each $2/5 = 0.4$, whereas the slopes of the diagonals of the green and red pieces are each $3/8 = 0.375$. Thus, while the shapes made by the top two and bottom two pieces may look like triangles, they are in fact concave quadrilaterals, which creates a thin white space between the pieces. This white space has area $1$, so the area, as expected, stays constant at $64$.

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