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Pythagorean Theorem proof in a 2100 year old Chinese book

346 点作者 balele大约 8 年前

13 条评论

jernfrost大约 8 年前
From what I understand, the Chinese had often recorded many facts about nature and mathematics very early and accurately. However they never really created much laws. Laws of nature was a western invention. E.g. they observed accurately planetary movements, but never attempted to formulate the laws governing those movements. That sort of thinking was crucial for scientific thinking.
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elevensies大约 8 年前
So if I'm understanding correctly, this is evidence that about 300 years after the death of Pythagoras, his proof "travelled" over the silk road to China?
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mariodiana大约 8 年前
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&#x27;s not the same thing as a proof: meaning, the fact has been integrated with the fundamentals of a wider body of knowledge.<p>I see the illustration, but I don&#x27;t understand how that&#x27;s a &quot;proof.&quot;
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happy-go-lucky大约 8 年前
<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Pythagorean_theorem" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Pythagorean_theorem</a><p>&gt; In India, the Baudhayana Sulba Sutra, the dates of which are given variously as between the 8th and 5th century BC, contains a list of Pythagorean triples discovered algebraically, a statement of the Pythagorean theorem, and a geometrical proof of the Pythagorean theorem for an isosceles right triangle.<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Baudhayana_sutras" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Baudhayana_sutras</a><p>&gt; A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together.<p>&gt; The lines are to be referring to a rectangle, although some interpretations consider this to refer to a square. In either case, it states that the square of the hypotenuse equals the sum of the squares of the sides.<p>&gt; If this refers to a rectangle, it is the earliest recorded statement of the Pythagorean theorem.
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lacampbell大约 8 年前
Wouldn&#x27;t something from that period be written with seal script? That script looks like modern Han characters with an archaic font - it&#x27;s completely readable.
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ajarmst大约 8 年前
It&#x27;s probably of value to note that that diagrams that everyone is talking about are not part of the original text.
gus_massa大约 8 年前
I don&#x27;t know Chinese, but I don&#x27;t like the explanation in English at the side. I think that both diagrams are part of the same proof, not two independent proofs. I agree with the first comment by Martin Cohen <a href="http:&#x2F;&#x2F;disq.us&#x2F;p&#x2F;1h6y5qx" rel="nofollow">http:&#x2F;&#x2F;disq.us&#x2F;p&#x2F;1h6y5qx</a><p>&gt; <i>The way I read it is that the first diagram says that(a+b)^2 = 4(ab&#x2F;2)+c^2 and the second says that c^2 = 4(ab&#x2F;2)+(a-b)^2. Both of these simplify to c^2 = a^2+b^2.</i><p>I only have a small proposed stylistic change that is to keep the are of the triangles as unknown values, let&#x27;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.<p>Is there a transcript and translation of the Chinese text?
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moomin大约 8 年前
I know you can use the second diagram to prove the theorem, but it requires an algebraic argument (the other two squares aren&#x27;t shown). Unless the text says something pretty interesting, this looks more like a proof just for a 3,4,5 triangle.<p>The first diagram I can&#x27;t get my head round at all, or is it proving something different?
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partycoder大约 8 年前
It was true then...<p><a href="http:&#x2F;&#x2F;abstrusegoose.com&#x2F;376" rel="nofollow">http:&#x2F;&#x2F;abstrusegoose.com&#x2F;376</a><p>However paper itself was invented around the same time. How come bookbinding already existed then?
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whatnotests大约 8 年前
Why not 2500 years ago!?
good_vibes大约 8 年前
Couldn&#x27;t have said it better myself. I think about this stuff a lot, how much ancient and modern overlap, how much Eastern and western overlap, yet how people still want to divide everything.<p>&quot;The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift.&quot; - Albert Einstein<p>&quot;The people in the Indian countryside don’t use their intellect like we do, they use their intuition instead, and the intuition is far more developed than in the rest of the world… Intuition is a very powerful thing, more powerful than intellect, in my opinion. That’s had a big impact on my work.<p>Western rational thought is not an innate human characteristic, it is learned and it is the great achievement of Western civilization. In the villages of India, they never learned it. They learned something else, which is in some ways just as valuable but in other ways is not. That’s the power of intuition and experiential wisdom.&quot; - Steve Jobs<p>Carl Sagan was really keen on seeing &#x27;the bigger picture&#x27; too, can&#x27;t find the particular quote I was looking for. Maybe later.
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lacampbell大约 8 年前
Any ideas of it&#x27;s authentic? China is hyper nationalist so I&#x27;m initially skeptical. Might be as fictitous as their GDP figures or sovereignty over Taiwan.
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chrishowlin大约 8 年前
I worry that China is outcompeting us.
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