Pythagorean theorem

If the two right-angled sides of a right-angled triangle are a, b, and the hypotenuse is c, then a2+b2=c2.i.e., the sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse.

The first solution of arithmetic has been written by Zhang Jie, naturally, he is not a master of arithmetic, and even arithmetic is convenient, Zhang Jie's previous life can only be regarded as a so-so level, belonging to the kind of many arithmetic problems that seem to understand but do not understand, but, even if it is just like this, for this world, Zhang Jie can already be regarded as a real arithmetic master. Pen, fun, pavilion www. biquge。 info Don't say anything else. With a simple Pythagorean theorem, Zhang Jie took out this junior high school knowledge point and asked people about it, but no one could solve it at all.

The shorter right-angled side in a right-angled triangle is called a hook, the longer right-angled side is called a strand, and the hypotenuse is called a chord, i.e., hook 2 + strand 2 = chord 2.

This is the formula of the Pythagorean theorem, when Zhang Jie showed this formula to the old master, the old man who had handed in books for decades just glanced at it and immediately waved his hand to admit defeat.

In the words of the old master, this kind of mysterious and mysterious thing is not suitable for his old man to blink an eye, this kind of thing, only Old Man Meng may know something.

Hearing that the old man Meng would actually count back, Zhang Jie immediately drove to visit, and after arriving in Mengjia Village, without saying a word, he directly took out the Pythagorean theorem, which reflects the quantitative relationship between the three sides of a right triangle, so it is the property theorem of the right triangle, which provides a new way for us to use the method of calculation to study the properties of geometric figures.

Then, let Old Man Meng prove that the proof of the Pythagorean theorem is commonly proved by the area method.

Old man Meng was really not a mortal, so he first took out a choice, and then said while sketching on the paper with a brush:

"The Pythagorean theorem only applies to right triangles, and this relationship does not exist for non-right triangles in general. The effect of the Pythagorean theorem is: the two sides of a known right triangle find the third side; In a right-angled triangle, one side is known, and the relationship between the other two sides is found; used to prove the squared relationship; Using the Pythagorean theorem, a long line segment is made. ”

Seeing that what Old Man Meng said was the Tao, Zhang Jie couldn't help but sigh slightly, it seems that it is impossible for him to fool people with this knowledge, because some people know these things, and they know even better than themselves, groaning slightly, Zhang Jie said:

"The Pythagorean theorem has a long history and contains rich cultural values. The Pythagorean theorem is a great theorem in the history of mathematics, which has a wide range of applications in real life and is known as the "first theorem of the ages". ”

When the old man Meng stopped, he saw that the old man's rice paper was densely packed with words, and when Zhang Jie glanced at it casually, he saw that it was written:

"The Pythagorean theorem reflects the trilateral relationship of a right triangle (the three sides are a, b, c, where c is the hypotenuse), i.e., c2 = a2 + b2, and its deformation is c2-a2 = b2 or c2-b2 = a2!"

Now that Old Man Meng has finished writing everything that should be written, Zhang Jie shook his head and sighed, then took out another piece of rice paper and wrote on the rice paper casually:

"It can be used to find the third side from the length of two sides in a right triangle. It is known that the length of the two sides of a right-angled triangle is 3cm and 4cm respectively, and the length of the third side is found, because the problem does not specify which side is the hypotenuse of the right-angled triangle, so it is necessary to classify and discuss, when the two right-angled sides are 3cm and 4cm respectively, the hypotenuse side is = 5cm by the Pythagorean theorem; When the hypotenuse is 4cm and the straight corner edge is 3cm, the other right-angled edge is. Therefore, the third side is 5cm or (root number) 7cm. ”

If the old man Meng wrote an overview, then Zhang Jie wrote the actual combat, and after Zhang Jie wrote all the theories and applications, he suddenly said to the old man Meng with a strange look: "How do you know about this thing?" You know, when I learned the solution to this problem from the great writer's house, I didn't suffer less, and in the end, when I paid enough price, I learned the ancestral solution from that person's house, and I also made a poisonous oath that I would never pass on the two of them in the future! ”

Seeing Old Man Meng say this, Zhang Jie immediately said strangely: "In this case, why did Uncle Meng break his oath today?" ”

Shaking his head slightly, the old man smiled and said: "I didn't tell you the solution, I just said something that is yes and no, the real solution, but you still gave it yourself, this is not a violation of the oath, besides, the great writer who forced me to make a poisonous oath back then has now declined, and these calculations may be slowly buried by these people, since you kid has a heart, I really want to pass on these knowledge!" It's all the wisdom left by the ancestors, but you can't just break the inheritance! ”

Old man Meng said sincerely, Zhang Jie knew that the old man really hoped that this knowledge could be passed on from generation to generation, not like now, this kind of advanced knowledge is only in the hands of a few people who cherish themselves behind closed doors.

At this time, Zhang Jie suddenly smiled and said: "Uncle Huang's don't have to regret, I'm afraid it won't be long before Uncle Huang's wish can be realized, this Pythagorean theorem is called the first law, and it is naturally going to be passed on. ”

Seeing that Zhang Jie was sure, Old Man Meng was also interested, and then asked, "The first solution to arithmetic?" What's that? Isn't it something you're messing around again? ”

Seeing the old man's distrustful look, Zhang Jie was dissatisfied: "What is a thing that fools people?" Do you think the Pythagorean theorem is subtle or not? Isn't it awesome? But I want to tell you, the law of consolidation, in the initial solution of arithmetic I wrote, can only be regarded as a reluctant, so-so existence, in my exercises, but there are many exquisite theories and exercises, just take out one, absolutely make you dumbfounded! ”

Naturally, Zhang Jie's stinky fart looked like Old Man Meng didn't believe it, and even Xiao Wu, who entered the door later, covered his mouth and chuckled.

Zhang Jie, who was immediately angry, picked up the rice paper at any time, and then wrote a few questions on the paper, threw the rice paper to the old man, and pointed to Zhang Jie, who had the above topic, and said casually:

"Don't believe it, if you can do anything about this topic, let me listen to you for anything! But if you can't do it, then promise me one condition, what do you think? (To be continued.) )