At the very start of the video you show two different "implementations" of Pythagoras's Theorem, which I took to be the same, as I didn't know that it was an evolution to joint geometry and algebra. If both representations are equivalent, I assume, that Euclidean Norm is implied. I also assume, that a right angled triangle is still the same if placed in a plane and moved around or rotated. Now the question: If I move the triangle and the shape changes, then the equivalence of both representations is no longer given. And is it right to say: an object changing shape when rotated is not an valid object under the algebraic and geometric relationship? (I know the wording is not "conventional" as math and English is not my native language ;-) )
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