The method of proving numbers by shapes is also used. Just move Zhu Fang's I(a2) to I', Fang Qing's II to II', and III to III', a square (c2). Just spell with the chord as the side. 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.

Only the specific division, combination and supplement are slightly different. Liu Hui's proof also has a picture, but unfortunately, the picture has been lost, leaving only a paragraph: "The hook is self-multiplied by Zhu Fang, and the stock is self-multiplied by Fang Qing, so that the entry and exit complement each other, each according to its type, because the rest are motionless, and the force of harmony. If the roots are divided, they are also chords. " Later generations made up a picture according to this paragraph.

The triangle is a right triangle, the square with hook A as the side is Zhu Fang, and the square with chain B as the side is square. Zhu Fang and Fang Qing were combined into a string phalanx. According to its area relationship, there is a+b = C. Because Zhu Fang and Fang Qing each have a part in the chord, that part will not move. ?

The square with the hook as the edge is Zhu Fang, and the square with the rope as the edge is Fang Qing. To make up for the deficiency, just move Zhu Fang's I(a2) to I', Fang Qing's II to II', and III to III', a square with the chord as the side length (the square of C? ). It can be proved that the square of A+the square of B = the square of C?

This proof was put forward by Liu Hui, a mathematician of Wei State in the Three Kingdoms period. In Wei Jingyuan four years (that is, 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 used "green out" and "Zhu out" to represent yellow, purple and green, and "green in" and "Zhu in" to explain how to fill the blank part of the hypotenuse square, later mathematicians called this figure "green in and out". Others use the word "complementarity" to express the principle of this proof.