41–50 of 153 posts
My understanding is that the 3-4-5 relationship was known for a long, long time before Pythagorus. I think the ancient Egyptians knew of the relationship. But that's not the same thing as a proof: meaning, the fact has been integrated with the fundamentals of a wider body of knowledge. I see the illustration, but I don't understand how that's a "proof."
Earlier quoted context omitted.
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.
Both diagrams are a proof over all right-angle triangles, if you know algebra. See the very first comment after the images.
But also, we can't trust geometrical diagrams: https://en.wikipedia.org/wiki/Missing_square_puzzle
My understanding is that the 3-4-5 relationship was known for a long, long time before Pythagorus. I think the ancient Egyptians knew of the relationship. But that's not the same thing as a proof: meaning, the fact has been integrated with the fundamentals of a wider body of knowledge. I see the illustration, but I don't understand how that's a "proof."
Also, Pythagoras was ~2500 years ago, before this thing.
Earlier quoted context omitted.
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…
It must be clarified that mainland of China is also part of ROC according to ROC government[1]. In fact, the mainland and taiwan are in war, just like the Union and Confederacy in American civil war, even if there is not military conflicts right now. More interestingly, ROC actually claims larger territory than PRC (for example, part of Mongolia). It is ROC's constitution, not PRC's government, demands taiwan is part…
Any ideas of it's authentic? China is hyper nationalist so I'm initially skeptical. Might be as fictitous as their GDP figures or sovereignty over Taiwan.
When you want to like Taiwan more but then notice their view of Tibet is just as twisted District 13
Earlier quoted context omitted.
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've ended dates over this with Chinese girls. Inevitably they condescend to me about how "I'm just an American" that "can't understand the complicated situation," but that I should rest assured that "Taiwan is not a country, it is a Chinese province." Never mind the fact that I lived there, documented the sunflower protests, speak the language... As opposed to these girls that hadn't even visited the nation. Because…
> The way I read it is that the first diagram says that(a+b)^2 = 4(ab/2)+c^2 and the second says that c^2 = 4(ab/2)+(a-b)^2. Both of these simplify to c^2 = a^2+b^2.
I only have a small proposed stylistic change that is to keep the are of the triangles as unknown values, let's call it T. So the first diagram shows that (a+b)^2 = 4T + c^2 and the second that c^2 = 4T + (a-b)^2. And simplifying you get simplify to c^2 = a^2 + b^2.
Is there a transcript and translation of the Chinese text?
I worry that China is outcompeting us.
Although to be realistic I don't think China will ever outcompete the US. Not because I don't want them to, but simply because so many fundamentals count in Americas favor and against China. China is facing a demographic catastrophe. The US can easily grow its population with immigration and has plenty of land and natural resources to do so.
My understanding is that the 3-4-5 relationship was known for a long, long time before Pythagorus. I think the ancient Egyptians knew of the relationship. But that's not the same thing as a proof: meaning, the fact has been integrated with the fundamentals of a wider body of knowledge. I see the illustration, but I don't understand how that's a "proof."
That's an illustration of the proof. Here is a more modern, animated example: https://upload.wikimedia.org/wikipedia/commons/2/29/Pythagor... The Chinese proof looks more like this one though: https://i.stack.imgur.com/Ylzhg.gif There is also explanation in the annotations.
