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The proof looks perfectly clear to me, except for a typo; CG=CD should be CG=GD (which is correctly stated earlier). What needs explanation? (This doesn't seem appropriate for MathOverflow.)
– Andreas BlassJun 26 '10 at 17:31

Closed, please check the FAQ.
– Scott Morrison♦Jun 26 '10 at 18:24

Christian: on a side note, you may like the analogous elementary proof of the irrationality of the other classic number, the golden ratio. Since it verifies the relation x=1+1/x and 1<x<2, if x were rational, x=p/q with 0<q<p, then also x=q/(p-q), and 0<p-q<q so there is no minimal denominator, a contradiction.
– Pietro MajerJun 26 '10 at 18:33

4

-1 for not saying what the questioner doesn't understand...
– Yemon ChoiJun 26 '10 at 19:37

whatthe questioner doesn't understand... – Yemon Choi Jun 26 '10 at 19:37