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- How can 64 = 65? 8 answers
What's wrong with the puzzle in this video?
I didn't understand. Do you understand what happens?
(Click the image to open the video)
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marked as duplicate by Dan Russell, Engineer Toast, Gamow, Deusovi♦ Aug 9 '16 at 21:00
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2$\begingroup$ 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 '16 at 17:12
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Obviously, $64\neq65$. Observe the diagram below:
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 $64$.
