送交者: 美女 于 2005-4-28, 02:52:30:
回答: 黎日工这次可错大了。 哈哈。 由 雅诗 于 2005-4-27, 16:16:19:
What's wrong?
Let Sa, Sb and Sc denote the area of the two smaller triangle and the whole. Obviously Sc = Sa + Sb.
Because all three triangles are similar, Sa : Sb : Sc = a^2 ： b^2 ： c^2.
The rest follows trivially. You don't really need any picture.
The property about the ratio of triangles of course uses the the 5th postulate , as it must.
I am not sure whether this is what 东郭 had in mind. He might have wanted to make fun of 黎日工 but the joke turned on himself. In special relativity, Pythagoras' theorem is not really a theorem but a definition of the (indefinite) metric of the underlying space.