A feature I find fascinating about this is that it demonstrates the internal consistency of maths. Once you get to the square of sides a+b at about 0:43, you can also get to the formula through a more algebraic path if that is your jam, but the important part is that if math is internaly consistent the two results must be equal in the end. And of course they are. The big square's area is (a+b)^2, which is the sum of the c^2 square and the the area of each of the 4 triangles which is ([a+b]^2)/2, so if you set the equation (a+b)^2 = 4 * ([a*b]/2 ) + c^2, develop it, isolate C^2 and simplify, you get exactly c^2 = a^2 + b^2 that way too.
Perhaps the best.... though I think I prefer the first one I animated (and the next one will use Thales triangle theorem, and I like that one quite a bit too).
@@MathVisualProofs , I needed rewind and pauses to deduce why the vertices of triangles should merge (so that the shaded area is a rectangle instead of a hexagon, say) after those shifts and rotations, at time around 0:50. Now i got it..thx
@@rgudduu Ah yes! definitely requires thought about why this forms a square (because the two angles are complementary and so the missing angle must be 90 at each place).
![Pythagoras Would Be Proud: High School Students' New Proof of the Pythagorean Theorem [TRIGONOMETRY]](http://i.ytimg.com/vi/p6j2nZKwf20/mqdefault.jpg)
A feature I find fascinating about this is that it demonstrates the internal consistency of maths. Once you get to the square of sides a+b at about 0:43, you can also get to the formula through a more algebraic path if that is your jam, but the important part is that if math is internaly consistent the two results must be equal in the end. And of course they are. The big square's area is (a+b)^2, which is the sum of the c^2 square and the the area of each of the 4 triangles which is ([a+b]^2)/2, so if you set the equation (a+b)^2 = 4 * ([a*b]/2 ) + c^2, develop it, isolate C^2 and simplify, you get exactly c^2 = a^2 + b^2 that way too.
My favorite proof of the Pythagorean theorem!
Perhaps the best.... though I think I prefer the first one I animated (and the next one will use Thales triangle theorem, and I like that one quite a bit too).
谢谢！
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theres no reason why math should be overhated
Perfect !!!!👏👏👏🙌
Glad you like it!
This is awesome!
Thanks so so much!!!!!!!
You're welcome!
Fundaments.
wow
Didn't understand
What part?
@@MathVisualProofs , I needed rewind and pauses to deduce why the vertices of triangles should merge (so that the shaded area is a rectangle instead of a hexagon, say) after those shifts and rotations, at time around 0:50. Now i got it..thx
@@rgudduu Ah yes! definitely requires thought about why this forms a square (because the two angles are complementary and so the missing angle must be 90 at each place).
BUT WHY!!!??
Why not?