(November 22, 2018 at 3:14 am)FlatAssembler Wrote: So, what do you think, is the Proof by Rearrangement of the Pythagorean Theorem valid? I've made a SVG animation presenting it here:
http://flatassembler.000webhostapp.com/p...ences.html
At first, it seems to make perfect sense. However, as I was making that animation, it appeared to me that it's actually a form of circular reasoning. Namely, how is it possible to prove that the angles of the c*c square are actually right angles, without appealing to the Pythagorean Theorem itself and the formula for the area of a parallelogram (P=a*b*sin(alpha))? It appears to me that it isn't.
You need to know the angles of a triangle add up to two right angles. That is enough to show that the central figure is a square.
To show the angles of a triangle add up to two right angles requires results on opposite interior and opposite exterior angles for parallel lines.
Those results require the parallel postulate.
