4 ms·

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 t

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."

dheera 10y ago
Also, Pythagoras was ~2500 years ago, before this thing.
- ekianjo 10y ago
  Exactly, by the time this book existed 2100 years ago, the idea should have been traveling all over the place anyway. It's not like ancient civilizations were not connected at all.
  - pjmlp 10y ago
    Yes, people travelled a lot, specially merchants, that is also how Alexandria got many of its manuscripts. The biggest difference was that nothing was assured about the safety of the travel.
Houshalter 10y ago
>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/Pythagorean_Theorem_Proof.gif 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 https://i.stack.imgur.com/Ylzhg.gif There is also explanation in the annotations.
- gravypod 10y ago
  It's mind blowing when I see a new image like that and it completely changes how I understand the topic. I wish I could find more of those.
  - pash 10y ago
    Search for the phrase "proofs without words" [0, 1]. There's long been a column in Mathematics Magazine by that name featuring proofs in this style, and there is a book of the same title published by the Mathematical Association of America (which I think collects proofs from the magazine column). Lots of examples from other sources will also show up in a web search. 0. https://encrypted.google.com/search?hl=en&q=proofs%20without%20words https://encrypted.google.com/search?hl=en&q=proofs%20without... 1. Image results: https://encrypted.google.com/search?q=proofs+without+words&num=30&hl=en&prmd=visn&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiC6Kf95vDSAhVK4YMKHZpjCPIQ_AUICCgC&biw=1024&bih=704 https://encrypted.google.com/search?q=proofs+without+words&n...
- y2kenny 10y ago
  This reminds me of this children toy: https://zh.wikipedia.org/wiki/%E4%B8%83%E5%B7%A7%E6%9D%BF https://zh.wikipedia.org/wiki/%E4%B8%83%E5%B7%A7%E6%9D%BF
johncolanduoni 10y ago
The 3-4-5 relationship is also merely a special case of the Pythagorean theorem, even if they had a proof that all such triangles are right triangles.

dheera 10y ago

Also, Pythagoras was ~2500 years ago, before this thing.

ekianjo 10y ago
Exactly, by the time this book existed 2100 years ago, the idea should have been traveling all over the place anyway. It's not like ancient civilizations were not connected at all.
- pjmlp 10y ago
  Yes, people travelled a lot, specially merchants, that is also how Alexandria got many of its manuscripts. The biggest difference was that nothing was assured about the safety of the travel.

Houshalter 10y ago

>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/Pythagorean_Theorem_Proof.gif 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 https://i.stack.imgur.com/Ylzhg.gif There is also explanation in the annotations.

gravypod 10y ago
It's mind blowing when I see a new image like that and it completely changes how I understand the topic. I wish I could find more of those.
- pash 10y ago
  Search for the phrase "proofs without words" [0, 1]. There's long been a column in Mathematics Magazine by that name featuring proofs in this style, and there is a book of the same title published by the Mathematical Association of America (which I think collects proofs from the magazine column). Lots of examples from other sources will also show up in a web search. 0. https://encrypted.google.com/search?hl=en&q=proofs%20without%20words https://encrypted.google.com/search?hl=en&q=proofs%20without... 1. Image results: https://encrypted.google.com/search?q=proofs+without+words&num=30&hl=en&prmd=visn&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiC6Kf95vDSAhVK4YMKHZpjCPIQ_AUICCgC&biw=1024&bih=704 https://encrypted.google.com/search?q=proofs+without+words&n...
y2kenny 10y ago
This reminds me of this children toy: https://zh.wikipedia.org/wiki/%E4%B8%83%E5%B7%A7%E6%9D%BF https://zh.wikipedia.org/wiki/%E4%B8%83%E5%B7%A7%E6%9D%BF

johncolanduoni 10y ago

The 3-4-5 relationship is also merely a special case of the Pythagorean theorem, even if they had a proof that all such triangles are right triangles.