Pythagorean Theorem: In any right triangle, the sum of the squares of the two right-angled sides must be equal to the square of the hypotenuse.
This theorem is also called the "Shang-Gao Theorem" in China and the "Pythagoras Theorem" in foreign countries. Why does one theorem have so many names? Shang Gao was a Chinese in the eleventh century BC. The Chinese dynasty at that time was the Western Zhou Dynasty, which was a period of slave society. In ancient China, the "Zhou Bi Suan Jing", a mathematical work written around the Western Han Dynasty during the Warring States Period, records a conversation between Shang Gao and Zhou Gong. Shang Gao said: "? Therefore, when bending, the hook is three, the strand is four, and the meridian is five." What are "hooks and strands"? In ancient China, people called the upper part of the arm bent at a right angle " "hook", the lower part is called "share". What Shang Gao's words mean is that when the two right-angled sides of a right triangle are 3 (short side) and 4 (long side) respectively, the radius corner (that is, the chord) is 5. From now on, people will simply refer to this fact as "hook three strands four strings five". Since the content of the Pythagorean Theorem was first seen in Shang Gao's words, people called this theorem "Shang Gao Theorem". Pythagoras was an ancient Greek mathematician who lived in the fifth century BC and was born more than five hundred years after Shang Gao. Another Greek mathematician, Euclid (Euclid, who lived around 300 BC), when compiling "Elements of Geometry", believed that this theorem was first discovered by Pythagodas, so he put this theorem into It was called "Pythagoras' theorem" and it became popular later.
Regarding the discovery of the Pythagorean theorem, "Zhou Bi Suan Jing" said: "Therefore, the reason why Yu ruled the world was the origin of this number." "This number" refers to "Gou" "Three strands, four strings and five", this sentence means: hooking three strands, four strings and five. This relationship was discovered by Dayu when he was controlling the floods.
The Pythagorean Theorem has a wide range of applications. Another ancient book from the Warring States Period in my country, "Twelve Notes to the Postscript of Lu Shi" contains this record: "Yu controlled the floods and cut off the rivers. He looked at the shapes of the mountains and rivers, determined the high and low trends, eliminated monstrous disasters, and directed the waters into the East China Sea. There is no danger of drowning, so this Pythagorean phenomenon is related to life. "The meaning of this passage is that in order to control floods, Dayu made rivers flow freely, determined the direction of water flow according to the height of the terrain, and took advantage of the situation to make the flood flow into the sea. , there will no longer be flood disasters, which is the result of applying the Pythagorean theorem.