Hook 2+ rope 2= chord 2
a2+b2=c2
Pythagoras theorem is called Pythagoras theorem in the west, and it is said that Pythagoras, a mathematician and philosopher of Pythagoras, first discovered it in 550 BC. In fact, this mathematical theorem was discovered and applied in ancient China much earlier than Pythagoras. If it can't be verified that Dayu's flood control is a long time ago, then the dialogue between Duke Zhou and Shang can be determined in the Western Zhou Dynasty around 1 100 BC, more than 500 years earlier than Pythagoras. Hooking 3 strands, 4 strings and 5 strings is a special application of Pythagorean theorem (32+42=52). So it should be very appropriate to call it Pythagorean Theorem in the field of mathematics now.
In the later book "Nine Chapters of Arithmetic", Pythagorean Theorem got a more standardized general expression. The book Gou Gu Zhang said: "Multiply the hook and the stock separately, then add up their products and make a square root, and you can get the string." Put this passage into an equation, that is:
Chord = (hook 2+ rope 2)( 1/2)
c=(a2+b2)( 1/2)
Mathematicians in ancient China not only discovered and applied Pythagorean Theorem very early, but also tried to prove Pythagorean Theorem in theory very early. Zhao Shuang, a mathematician of the State of Wu in the Three Kingdoms period, was the first to prove the Pythagorean theorem. Zhao Shuang created "Pythagorean Square Diagram" and gave a detailed proof of Pythagorean theorem by combining shape and number. In this Pythagorean Square Diagram, the square ABDE with the chord as the side length is composed of four equal right triangles and a small square in the middle. The area of each right triangle is AB/2; If the side length of a small square is b-a, the area is (b-a)2. Then you can get the following formula:
4×(ab/2)+(b-a)2=c2
After simplification, you can get:
a2+b2=c2
c=(a2+b2)( 1/2)