Posted by Eugene Volokh:
64 = 65 math puzzle:
A reader asks: "[C]an you explain [1]this geometry puzzle?," pointing
to the 8 x 8 = 5 x 13 puzzle that's been making the rounds. He adds:
Ever since I saw it, I've had a hard time concentrating on work. It
seems to call into question an orderly universe, which is quite
disturbing.
Well, I surely don't want American productivity -- or for that matter
American faith in an orderly universe -- to decline. So the answer is
[2]available by clicking here.
The diagonals of the blue shape and the green shape (and likewise of
the red and the orange) in the 5 x 13 figure look like they match up,
but they actually don't. There's a narrow gap between them, too narrow
to see easily, but when it's added up over the length of the 5 x 13
figure, it amounts to the missing square. The slope of the bottom of
the blue shape is 5/2 = 2.5; the slope of the top of the green shape
is 8/3 = 2.666....
At x=5, for instance, the blue shape's y=2, but the green shape's
y=5x3/8=15/8. The 1/8 difference between 2 and 15/8 is the gap I told
you about. ([3]hide)
References
1. http://www.blessa.com/64-equals-65.gif
2. file://localhost/var/www/powerblogs/volokh/posts/1093524465.html
3. file://localhost/var/www/powerblogs/volokh/posts/1093524465.html
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