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Originally Posted by TINNY
so how can euclidian geometry be simultaneously right and wrong? It has to be either one of the two. Refering to Bo, it is a matter of application and suitability.
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Like Bo said: it has to do with dimensions. Euclid wrote his books in a 3D world with no knowledge of curved space. So for him, any triangle must have corners which make 180 degrees. This is still true, but only on a flat enough area (a piece of paper, say).
If you take a globe of the Earth and try to draw a perfect triangle on it you will see that it sums up to more than 180 degrees, becase of the curvature of the Earth.
So Euclid was not wrong. It's the same with Newton - he believed in action at a distance (instant action of gravity, say, between the Sun and the Earth) but Einstein proved this not to be the case. Yet we still use Newton's laws because generally they work, except when you need the laws of relativity.
It's about choosing the right tools for the job, basically.