A simple proof that √2 is irrational
AUTHOR: Stanley Tennenbaum
#QUARK
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Placing the 2 smaller squares on the larger one, we see that the sum of the areas of the corner squares must equal the area of the black central one. We reached a contradiction since we assumed a and b are the smallest integers such that a²=2b²!pic.twitter.com/2xMt3MN2zL
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I like this better: assuming a²=2b², write out a and b as products of primes. Then the equation means there is an even number of primes on one side and an odd number of primes on the other. Contradicts fundamental theorem of arithmetic. :-)
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... and that proof holds for all primes, not just 2.
End of conversation
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Didn’t Hippasus get thrown overboard for this? Be safe out there!
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