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HP Forum Archive 20

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64 = 65 ???
Message #1 Posted by Erturk Kocalar on 19 Feb 2012, 3:08 p.m.

My dad forward this to me. It proves 64 = 65. Not really. It took me 10 seconds to figure out what's wrong.

http://img7.exs.cx/img7/6534/1388.gif

I did click on the link; I'm using mac os; my computer is still fine. (If you are using windows, please click at your own risk.)

enjoy.

Edited: 19 Feb 2012, 3:09 p.m.

      
Re: 64 = 65 ???
Message #2 Posted by C.Ret on 19 Feb 2012, 3:15 p.m.,
in response to message #1 by Erturk Kocalar

Ah! Ah!

That's a well know property, moving any colored shape makes algebra wrong !

Another illustration :

Edited: 19 Feb 2012, 3:17 p.m.

            
Re: 64 = 65 ???
Message #3 Posted by Erturk Kocalar on 19 Feb 2012, 3:31 p.m.,
in response to message #2 by C.Ret

Very cool. I haven't seen these before.

            
Re: 64 = 65 ??? (solution)
Message #4 Posted by Dieter on 19 Feb 2012, 3:39 p.m.,
in response to message #2 by C.Ret

All this - especially the well known property of moving colored shapes making algebra wrong ;-) - works because our eyes simply do not work sufficiently accurate to distinguish two very similar, yet different slopes in the red/green and blue/orange shapes (first example) resp. the red and green triangles in the second example.

If you look more closely you'll notice that the slopes of the mentioned shapes are slightly different, so they cannot be arranged the way the final layout suggests. One the one hand it's 3:8 boxes, on the other hand it's 2:5. In other words: 0,375 vs. 0,4. Which is so close that the difference it is not obvious for the human eye.

Dieter

            
Re: 64 = 65 ???
Message #5 Posted by Gerson W. Barbosa on 19 Feb 2012, 7:48 p.m.,
in response to message #2 by C.Ret

This picture might disprove the equality:

Another interesting illusion:

http://alexbellos.com/?p=742

                  
Re: 64 = 65 ???
Message #6 Posted by Paul Dale on 19 Feb 2012, 7:54 p.m.,
in response to message #5 by Gerson W. Barbosa

Quote:
Another interesting illusion:

http://alexbellos.com/?p=742


Lovely. I'd not seen this one before.

- Pauli

                        
Re: 64 = 65 ???
Message #7 Posted by Ed Look on 20 Feb 2012, 3:44 p.m.,
in response to message #6 by Paul Dale

Way cool!!

All of these are fascinating!


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