31–40 of 153 posts
Earlier quoted context omitted.
It could've been used without being proved also
The diagrams on the pages shown basically serve as a proof.
Wouldn't something from that period be written with seal script? That script looks like modern Han characters with an archaic font - it's completely readable.
The first diagram I can't get my head round at all, or is it proving something different?
Earlier quoted context omitted.
The diagrams on the pages shown basically serve as a proof.
It's familiar from hands-on science museums to see a particular case of the Pythagorean theorem illustrated concretely with diagrams or liquid on a rotating plexiglass panel... But surely those aren't proofs, just illustrations. A proof needs to abstract over all possible right-angle triangles.
Earlier quoted context omitted.
> sovereignty over Taiwan This is the claim that China and Taiwan should reunite since the PRC drove the Nationalist Party out of mainland China. It isn't fictitious, it's merely a political wish to merge the two from the PRC side. Similarly, some Nationalists in Taiwan are happy to take back mainland China, as much as the country is divided on whether Taiwan should remain as it is, or should declare its full indepen…
Doesn't the PRC's claim on Taiwan boil down to a combination of right-of-conquest ("Taiwan belonged to the Republic of China, we beat up the Republic of China, therefore Taiwan is ours") and Just Because? ("The PRC is the only legitimate Chinese government because the PRC says so") I'm very skeptical of purely historical claims of sovereignty. If the people of Taiwan legitimately vote to join the PRC, that's their ri…
[1] https://commons.wikimedia.org/wiki/File:ROC_Administrative_a...
Earlier quoted context omitted.
> sovereignty over Taiwan This is the claim that China and Taiwan should reunite since the PRC drove the Nationalist Party out of mainland China. It isn't fictitious, it's merely a political wish to merge the two from the PRC side. Similarly, some Nationalists in Taiwan are happy to take back mainland China, as much as the country is divided on whether Taiwan should remain as it is, or should declare its full indepen…
The GP is talking about the straight-faced lie that the PRC peddles in international circles that Taiwan is a province of the mainland government. It is the international equivalent of putting their hands on their ears and shouting "LA LA LA I CAN'T HEAR YOU!", and about as legitimate as Mexico's claim to Texas.
I know you can use the second diagram to prove the theorem, but it requires an algebraic argument (the other two squares aren't shown). Unless the text says something pretty interesting, this looks more like a proof just for a 3,4,5 triangle. The first diagram I can't get my head round at all, or is it proving something different?
I see the illustration, but I don't understand how that's a "proof."
I know you can use the second diagram to prove the theorem, but it requires an algebraic argument (the other two squares aren't shown). Unless the text says something pretty interesting, this looks more like a proof just for a 3,4,5 triangle. The first diagram I can't get my head round at all, or is it proving something different?
If we label the sides a=3, b=4, and c=5 :
The first diagram shows that the big outer square of length (a+b) equals the area of the 4 triangles plus the rotated square of side c. (a+b)^2 = 2ab + c^2
[I'm not sure why they drew an inner 3x3 square on its own].
The second diagram puts the same four triangles inside the rotated square of side c, which leaves an extra smaller square of side (b-a) inside.
c^2 = 2ab + (b-a)^2
