Root 2 irrationality proof (geometric)

  • Thread starter phospho
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I was looking over this proof and I have some questions:

http://jeremykun.com/2011/08/14/the-square-root-of-2-is-irrational-geometric-proof/

Second paragraph, what does "swinging a b-leg to the hypotunese" mean? Also, where did the arc come from, I really don't understand

also, the last part ## \dfrac{2b-a}{a-b} ## how does this lead to a contradiction (i.e. how is 2b-a and a-b smaller than a and b?

really don't understand the proof overall, if someone could walk me through it or give me some pointers it'd really help thank you
 

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  • #2
tiny-tim
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hi phospho! :smile:
Second paragraph, what does "swinging a b-leg to the hypotunese" mean? Also, where did the arc come from, I really don't understand
it's a really stupid way of saying "draw an arc of a circle of radius b from R to the hypotenuse" :redface:
i.e. how is 2b-a and a-b smaller than a and b?
2b - a = b + (b -a), which is obviously < b :wink:

(and a - b < a)
 

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