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Author Topic: 64 = 65? Joe Redifer You need a beating today Posts: 12859 From: Denver, Colorado Registered: May 99 posted 03-12-2004 01:36 AM                         |  IP: Logged Gilbert Travin Expert Film Handler Posts: 101 From: Villeurbanne / France Registered: Jan 2004 posted 03-12-2004 01:53 AM                        Hi Joe ! The apparent contradiction is perhaps a problem of rounding when boxes are divided?  |  IP: Logged Daryl C. W. O'Shea Film God Posts: 3977 From: Midland Ontario Canada (where Panavision & IMAX lenses come from) Registered: Jun 2002 posted 03-12-2004 01:58 AM                        Uh, those triangles wouldn't fit together like that, their slopes aren't the same. Close enough to fudge though.  |  IP: Logged Dustin Mitchell Phenomenal Film Handler Posts: 1865 From: Mondovi, WI, USA Registered: Mar 2000 posted 03-12-2004 02:11 AM                     *waits for Evans*  |  IP: Logged Daryl C. W. O'Shea Film God Posts: 3977 From: Midland Ontario Canada (where Panavision & IMAX lenses come from) Registered: Jun 2002 posted 03-12-2004 02:23 AM                        What for? We already know what the illusion is.  |  IP: Logged Wolff King Morrow Master Film Handler Posts: 490 From: Denton, TX, USA Registered: Feb 2004 posted 03-12-2004 02:29 AM                        Take particular note of the blue and green on the final joining. The 3rd square over from the left is extremely "estimated" and doesn't line up at all.  |  IP: Logged Brian Michael Weidemann Expert cat molester Posts: 944 From: Costa Mesa, CA United States Registered: Feb 2004 posted 03-12-2004 05:05 AM                        Yeah, look at those center three boxes in the 5x13 one, the horizontal lines on the tops and bottoms shift. If you were actually to cut these shapes out from the first and arrange the "5x13", there would be precisely one square unit of gap over that whole diagonal. Narrow, but definitely there. This wouldn't be convincing at all if the demonstration were larger and the shapes didn't use such a thick border. The slope shifts from 2/5 to 3/8 or vice versa at the joints. 0.4 versus 0.375 Close, but no cigar.  |  IP: Logged Manny Knowles "What are these things and WHY are they BLUE???" Posts: 4247 From: Bloomington, IN, USA Registered: Feb 2002 posted 03-12-2004 09:42 AM                     Yeah. I can't believe Joe actually fell for that. What a gullible idiot he is!  |  IP: Logged Tim Reed Better Projection Pays Posts: 5246 From: Northampton, PA Registered: Sep 1999 posted 03-12-2004 09:53 AM                       The angles/colors are there to throw you off. They cover the deception of your perception. Everyone knows you can't split your blocks. The real trick would be to make it work and stay within the squares!  |  IP: Logged Thomas Procyk Phenomenal Film Handler Posts: 1842 From: Royal Palm Beach, FL, USA Registered: Feb 2002 posted 03-12-2004 12:53 PM                     WTF? This thread is dumb. I don't see boxes or triangles or anything anyone is talking about. Just "64=65 ?" Explain before I condemn this thread to total stupidity! =TMP=  |  IP: Logged Mike Blakesley Film God Posts: 12767 From: Forsyth, Montana Registered: Jun 99 posted 03-12-2004 01:27 PM                        Brings to mind an old Mad Magazine "puzzle:" "Arrange these shapes into a square" The solution was to just throw the shapes into the square any old way, with the solution: "You probably couldn't make it work becauase you wouldn't overlap the shapes...but nobody said you couldn't, you dolt!"  |  IP: Logged Dustin Mitchell Phenomenal Film Handler Posts: 1865 From: Mondovi, WI, USA Registered: Mar 2000 posted 03-12-2004 02:58 PM                     I'm waiting for Evans to provide us with a essay utilizing multi-variable calculas to explain the problem, as opposed to your one line explanation Daryl .  |  IP: Logged Steve Kraus Film God Posts: 4094 From: Chicago, IL, USA Registered: May 2000 posted 03-12-2004 11:18 PM                    Thomas, it's an animation and you need to lower your shields to see it play.  |  IP: Logged Evans A Criswell Phenomenal Film Handler Posts: 1579 From: Huntsville, AL, USA Registered: Mar 2000 posted 03-16-2004 09:06 PM                        Joe emailed me and pointed out to me that I missed this thread. The pieces do not fit together perfectly when arranged, as several of you have pointed out. I first saw this kind of thing back in 1987 in the book "Aha: Insight". It involved a similar thing: a square rug of a certain size that could be cut up, almost exactly like the one shown in this thread, so that its rearranges size had an area that differed from the original by 1. It was a 13 by 13 (area 169) that rearranges into a 21 by 8 (area 168). Unless the pieces are cut with extreme precision, you won't notice that the pieces don't fit together perfectly (the beauty of real-life situations). This trick works with numbers from the Fibonacci sequence: Note that the one I saw years ago used numbers 5, 8, 13, 21. Any 4 consecutive Fibonacci numbers can be used if you go far enough into the sequence. The farther the better the actual fit (the more closely the slopes of the pieces of the triangles actually are to each other): 3 5 8 13 (8x8 rearranaged into a 5x13) 5 8 13 21 (13x13 rearranged into a 8x21) 8 13 21 34 (21x21 rearranged into a 13x34) and so on.  |  IP: Logged Dustin Mitchell Phenomenal Film Handler Posts: 1865 From: Mondovi, WI, USA Registered: Mar 2000 posted 03-16-2004 10:26 PM                     You see Daryl, that was much more interesting than your answer . Evans, thank you.  |  IP: Logged

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