According to textual research, human beings have known this theorem for at least 4000 years! It is also recorded that this theorem has more than 300 proofs all over the world!
Pythagorean theorem is a pearl in geometry, so it is full of charm. For thousands of years, people have been eager to prove it, including famous mathematicians, amateur mathematicians, ordinary people, distinguished dignitaries and even national presidents. Perhaps it is precisely because of the importance, simplicity and attractiveness of Pythagorean theorem that it has been repeatedly hyped and demonstrated for hundreds of times. 1940 published a proof album of Pythagorean theorem, which collected 367 different proof methods. In fact, that's not all. Some data show that there are more than 500 ways to prove Pythagorean theorem, and only the mathematician Hua in the late Qing Dynasty provided more than 20 wonderful ways to prove it. This is unmatched by any theorem.
Proof of Pythagorean Theorem: Among these hundreds of proof methods, some are very wonderful, some are very concise, and some are very famous for their special identities.
Firstly, the two most wonderful proofs of Pythagorean theorem are introduced, which are said to come from China and Greece respectively.
1. China method: draw two squares with side length (a+b), as shown in the figure, where a and b are right-angled sides and c is hypotenuse. The two squares are congruent, so the areas are equal.
The left picture and the right picture each have four triangles that are the same as the original right triangle, and the sum of the areas of the left and right triangles must be equal. If all four triangles in the left and right images are deleted, the areas of the rest of the image will be equal. There are two squares left in the picture on the left, with A and B as sides respectively. On the right is a square with C as its side. therefore
a^2+b^2=c^2。
This is the method introduced in our geometry textbook. Intuitive and simple, everyone can understand.