Pythagorean proof found on 2000 year old Chinese scroll.

[thechamp]

Can anyone understand this?!

 

I can't at all!

 

http://fermatslibrary.com/s/pythagorean-theorem-proof-in-zhoubi-suanjing#email-newsletter

 

[imron]

a² = b² + c²

[lips]

It's an illustration from 《周髀算经》,a Han dynasty mathematical treatise, which quoted a discussion of the Pythagoras theorem and its proof from early Zhou dynasty (3,500 years ago).  The picture originally had different colours (hence the characters 朱、黄).  勾 refers to the shorter arm of the right angle, 股 is the longer arm of the right angle, and 弦 is the hypotenuse.  You can see the 3-4-5 right angle triangle labeled in the bottom left of the second picture.  I think 實 means area.  The Chinese name of the theorem is 勾股定理。

 

This is a famous drawing, and was the logo of the 2002 International Congress of Mathematicians (ICM).

 

Not that the Chinese being the discoverer of the theorem.  It was well-known in the ancient world, including the Egyptian and Babylonians.

[lips]

For those who want to practice reading classical Chinese:

 

http://baike.baidu.com/item/勾股定理

 

[lips]

First picture，  LHS:  股實之矩十六黄――the area of the square on the longer arm is 16 and is coloured yellow.  RHS:  勾實九青――the area on the shorter arm is 9 and is coloured blue.