Dont’t you mean √2=(2b-a)/(a-b) instead of √2=(2a-b)/(a-b)???
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Omitting steps and saving punctuation marks just to fit into a single tweet doesn’t add to the educational value.
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Help! How do we know that sum of areas of uncovered square was equal to overlapped area?
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Both the large carpet (a^2) and the 2 small carpets (2×b^2) must fill the room. Where the small ones overlap, they are "double", and in the corner "none". So, the doubly covered area must be equal to the uncovered area. This had me too, at first...
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The first = should be a +, no?
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I thought so at first, based on it talking about the sum > Since the sum of the overlap and uncovered areas is equal But now I'm having trouble parsing that... Seems it should read > Since the sum of uncovered areas is equal to the overlap Or else rest doesn't follow...
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Why is a-b < b? One proof is by contradiction: if a-b >= b, then a >= 2b, which implies that (a/b)^2 >= 4 > 2
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a,b are supposed to be integers (even if not explicitly stated in the tweet)
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It could have been proven much simpler. If you square both sides, you’ll get 2b^2=a^2. This means a and therefore b are even but this contradicts our assumptions which says a and b does not have any common factor (lowest term).
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How does 2b^2 = a^2 mean b is even?
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