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Steven Strogatz
Elegant proof that the square root of 2 is irrational, by Stanley Tennenbaum & see the interesting comments & links
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Steven Strogatz 17. sij 2017.
Right! See comment by earlier in this thread
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Karel de Bruin 🇿🇦 17. sij 2017.
Odgovor korisniku/ci @stevenstrogatz
"But the dark blue square and the small pink squares have integer sides" -> how do we know this?
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Steven Strogatz 17. sij 2017.
Odgovor korisniku/ci @kareldebruin
. recall long pink side=a. Blue=b. So uncovered pink=a-b=whole #. And Dark blue+2(a-b)=a. Thus dark=2b-a=whole number too.
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Thomas 17. sij 2017.
Odgovor korisniku/ci @stevenstrogatz
Nice! This is the visual version of the inf descent proof: a/b = sqrt(2) --> (2b-a)/(a-b) = sqrt(2), with 0<2b-a<a, 0<a-b<b.
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Steven Strogatz 17. sij 2017.
Odgovor korisniku/ci @thomashorine
Exactly!
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Ido Roll 17. sij 2017.
Odgovor korisniku/ci @stevenstrogatz @marktmaclean
My favourite: √2=x/y (GCD=1); x^2/y^2=2; x^2=2y^2; x even; 4(x/2)^2=2y^2; 2(x/2)^2=y^2; y even; GCD=2 QED
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George Jelliss 17. sij 2017.
Odgovor korisniku/ci @stevenstrogatz @JohnAllenPaulos
Klein's String is quite well known. It is illustrated in Rouse Ball's Mathematical Recreations 1939 p.86.
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John Allen Paulos 17. sij 2017.
Odgovor korisniku/ci @mayhematics @stevenstrogatz
Thanks.
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