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Author Topic: 64 = 65? Brian Michael Weidemann Expert cat molester Posts: 944 From: Costa Mesa, CA United States Registered: Feb 2004 posted 03-17-2004 02:34 AM                        Oh, yes, the beauty of the Fibonacci sequence! Math rules!!!  |  IP: Logged Michael Schaffer "Where is the Boardwalk Hotel?" Posts: 4143 From: Boston, MA Registered: Apr 2002 posted 03-17-2004 03:01 AM                        Fibonacci? Isn`t that a pasta sauce?  |  IP: Logged Evans A Criswell Phenomenal Film Handler Posts: 1579 From: Huntsville, AL, USA Registered: Mar 2000 posted 03-17-2004 10:49 AM                        Today, since I'm in my office, I can provide better references to this subject. The title of the book where I first saw this phenomenon illustrated was aha! Gotcha: Paradoxes to puzzle and delight by Martin Gardner (1982). I got the book free one year (it came on March 18, 1986) when I subscribed to Scientific American. While at Jacksonville State University, I checked a book out of their library that had a chapter on this kind of thing (most likely, a Martin Gardner book). On the Fibonacci sequence, to generate it, just start with 0 and 1 and make each next number be the sum of the two numbers before it, like this: 0 1 1 2 3 5 8 13 21 34 55 89 144 ... The growth rate converges to the "golden ratio", which is equal to (sqrt(5) + 1) / 2 or 1.6180339887... After lunch, I'll scan a couple of things. I have another one of these "rearrange and get a different area" puzzle that's a bit harder to see.  |  IP: Logged Evans A Criswell Phenomenal Film Handler Posts: 1579 From: Huntsville, AL, USA Registered: Mar 2000 posted 03-17-2004 01:12 PM                        OK. Here are the diagrams from the book I mentioned. The first one (the top two figures) are like the one Joe used, except it uses a 13 by 13 rectangle rearranged into an 8 by 21 rectangle. The second one, however, uses a 12 by 12 rectangle with a 1 by 1 hole in it, which is rearranged into a 12 by 12 rectangle without a hole. I find the second one (bottom two figures) much more interesting. Feedback welcome! Here's the image:  |  IP: Logged Thomas Procyk Phenomenal Film Handler Posts: 1842 From: Royal Palm Beach, FL, USA Registered: Feb 2002 posted 03-18-2004 10:27 AM                     Fibonacci is the name of my friend's secksy cat. =TMP=  |  IP: Logged

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