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@stevenstrogatz | |||||
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Elegant proof that the square root of 2 is irrational, by Stanley Tennenbaum divisbyzero.com/2009/10/06/ten… & see the interesting comments & links pic.twitter.com/BIXMa0XfSh
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Steven Strogatz
@stevenstrogatz
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17. sij 2017. |
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Right! See comment by @thomashorine earlier in this thread
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Karel de Bruin 🇿🇦
@kareldebruin
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17. sij 2017. |
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"But the dark blue square and the small pink squares have integer sides" -> how do we know this?
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Steven Strogatz
@stevenstrogatz
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17. sij 2017. |
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.@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
@thomashorine
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17. sij 2017. |
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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
@stevenstrogatz
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17. sij 2017. |
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Exactly!
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Ido Roll
@hummus_monster
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17. sij 2017. |
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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
@mayhematics
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17. sij 2017. |
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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
@JohnAllenPaulos
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17. sij 2017. |
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Thanks.
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