When Liu Hui proved Pythagorean theorem, he also used the method of proving numbers in form, but the specific division, combination and complement were slightly different. Liu Hui's proof was originally a picture, but unfortunately the picture has been lost, leaving only a paragraph: "Hooking Zhu Fang, the shares are multiplied by the square, so that the entry and exit complement each other, and other things are the same, synthesizing the power of chords. In addition to roots, chords also. "
The square with the hook as the edge is Zhu Fang, and the square with the stock as the edge is Fang Qing. In order to win and make up for the shortcomings, just move Zhu Fang's I(a2) to I' and Fang Qing's II to II' and III' in the picture, and you will make a square (c2). Take the chord as the side length. It can be proved that a2+b2=c2.
This proof was put forward by Liu Hui, a mathematician of Wei State in the Three Kingdoms period. In the fourth year of Wei Jingyuan (AD 263), Liu Hui annotated the ancient book Nine Chapters Arithmetic. In the annotation, he drew a diagram similar to Figure 5 (b) to prove Pythagorean theorem. Because he represents yellow, purple and green in the chart,
The blue-red graph needs to be proved by the knowledge of triangle congruence.