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square pegs in round holes [message #477640] 
Sat, 02 October 2010 19:35 

Barbara Boehmer
Messages: 8922 Registered: November 2002 Location: California, USA

Senior Member 


We all do dumb things. I was a high school math major and can't believe that I messed up this simple geometry problem and was basically trying to put a square peg in a round hole. I must have been suffering from sleep deprivation and not paying attention at the time. I recently ordered some containers to fit inside some other containers that I already had. I thought I had checked all the measurements carefully. The outer containers are 15" high, tapered cylinders from 16" diameter at the top and 13" diameter at the bottom. The new containers are listed as 13.25"H x 12"Dx12"W. The height is not a problem. I thought the diameter, depth, width or whatever was not a problem, since the inner one is 12" and the outer one's minimum at the bottom is 13". Wrong! It turns out that the 12"Dx12"W is square, so the widest point is the diagonal or 17" and it doesn't fit, even at the wide top:
SCOTT@orcl_11gR2> select sqrt ((12 * 12) + (12 * 12)) from dual;
SQRT((12*12)+(12*12))

16.9705627
1 row selected.
SCOTT@orcl_11gR2>
[LF set [code] tags instead of [email] ones]
[Updated on: Sun, 03 October 2010 02:27] by Moderator Report message to a moderator




Re: square pegs in round holes [message #477663 is a reply to message #477656] 
Sun, 03 October 2010 04:24 
John Watson
Messages: 8301 Registered: January 2010 Location: Global Village

Senior Member 


What BB has demonstrated (though only peripherally) is that there are no isosceles Pythagorean triples. A Pythagorian triple is an example of three numbers related by Pythagoras' theorem, with the additional constraint that all numbers must be integers: 345, 51213, and so on. There is an infinite number of solutions, and the maths to generate them through Euclid's Formula and variations is not overly complex (though it is a little more advanced than LF's problem):
http://en.wikipedia.org/wiki/Pythagorean_triple
The reason for the impossibility of an isosceles Pythagorean triple comes from the fact that root two is a surd, and the longer side of any isosceles triangle can be expressed as the length of the shorter sides multiplied by this. In BBs case, root two times 12.



Re: square pegs in round holes [message #477697 is a reply to message #477663] 
Sun, 03 October 2010 19:03 
rleishman
Messages: 3728 Registered: October 2005 Location: Melbourne, Australia

Senior Member 


John, you strike me as the sort of chap who would enjoy Neal Stephenson novels. He explores science/computer/math themes such as viruses, AI, economics, cryptography, and quantum theory in works of actionpacked intelligent fiction.
For newcomers who enjoy both Science and Fiction, but not in the guise of what most would term "Science Fiction", then I recommend starting with the more recent Cryptonomicon (if you can't face 1000 page novels, best try another author). Earlier works such as Snow Crash and Diamond Age  whilst brilliant  are a little closer to a Science Fiction staple, although Stephenson prefers the term "Speculative Fiction".
The Baroque Cycle trilogy is arguably a Cryptonomicon prequel. They are essentially unrelated, but written and paced similarly to Cryptonomicon and use many of the same family names in different eras.
I am currently reading his most recent novel  Anathem.



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