Maybe I just had a bad day, I dunno.
Looking over some geometric proofs, one of them is discussing some constructable number, sqrt(4+sqrt(7+sqrt(2))). The proof that such a number is irrational I thought was clever. First you prove that the square root of 2 is irrational. Then you have r equal that number and simply solve for the square root of 2, assuming that r is a rational number. You find a contradiction there.
The geometric one is to show that a collapsing compass is mathematically equivalent to the modern compass by proving that you can copy circles using only a collapsing compass, something it cannot easily do unlike the modern compass. You use radii of circles as triangle side lengths and show that many triangles are congruent, and thus their angles are congruent. A bit time consuming but clever.
This post has been edited by Elnendil: Apr 23 2011, 02:24 PM
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QUOTE Kenji: Where else would I could get beaten with a phone that would make me unable to remember it? The ass?
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