Root 2 irrationality proof (geometric)

[phospho]

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

 

[tiny-tim]

hi phospho!

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"

i.e. how is 2b-a and a-b smaller than a and b?

2b - a = b + (b -a), which is obviously < b

(and a - b < a)