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Subject: "Irationality of root 2"     Previous Topic | Next Topic
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Conferences The CTK Exchange Thoughts and Suggestions Topic #57
Reading Topic #57
Aaron
guest
 Feb-20-09, 03:50 PM (EST)
 
"Irationality of root 2"
 
   There are already several versions of a geometric proof by infinite descent so maybe another isn't needed. BUT I did not see this version( maybe I overlooked it...) which is especially visually clear to people who are less scared by rectangles than by triangles (I'll describe rather than draw the diagram): Take a rectangle in proportions 1 to sqrt(2) (like an ideal sheet of A4 paper). Remove a largest square from the top leaving one with proportions 1 to sqrt(2)-1 along the base. Then remove a largest possible square from the right side of this smaller rectangle. The result is an even smaller rectangle proportional to the first. SO (as usual) the Euclidean algorithm never ceases.


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alexbadmin
Charter Member
2336 posts		 Feb-20-09, 05:02 PM (EST)
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2. "RE: Irationality of root 2"
In response to message #0
 
   Thank you. It is certainly worth mentioning.

What is your name? I'd like to give a credit.


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Aaron
guest
 Feb-20-09, 09:58 PM (EST)
 
3. "RE: Irationality of root 2"
In response to message #2
 
   Aaron Meyerowitz meyerowi@fau.edu

I suppose the smaller rectangle is rotated 90 degrees. Here is a link to a kind of hokey book The Elements of Dynamic Symmetry By Jay Hambidge which has a picture.

https://books.google.com/books?id=F4C6YelrRrEC&printsec=frontcover&dq=jay+hambidge&ei=bEqfSbnqGoLeyASrg5GMAg#PPA43,M1


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alexbadmin
Charter Member
2336 posts		 Feb-20-09, 09:59 PM (EST)
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4. "RE: Irationality of root 2"
In response to message #3
 
   Very good. Thank you.


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