Yes, but how do I know that really and truly is a tesselation? Maybe it doesn't work always. You only know that it's an accurate representation if you already know an awful lot of Euclidean geometry; so I don't think it's a proof without a little bit more annotation. (Sum of angles in a triangle is enough, which depends on opposite angles in intersecting lines, which is proved from the axioms, iirc.)
(Euclid, thou shoulds't be living at this hour!)
The algebraic proof is fine. I actually mark this stuff from first years, and the only thing missing is the axioms that justify each step - commutative addition, multiplication distributive over addition, and commutative multiplication.
Can you prove that there is only one 1? It's such a pretty thing...
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Date: 2005-04-04 11:58 am (UTC)(Euclid, thou shoulds't be living at this hour!)
The algebraic proof is fine. I actually mark this stuff from first years, and the only thing missing is the axioms that justify each step - commutative addition, multiplication distributive over addition, and commutative multiplication.
Can you prove that there is only one 1? It's such a pretty thing...