In fact, Liu Yong is worried in vain, according to the current level of science and technology, it is undoubtedly a fool's dream to build an ironclad warship. Pen & Fun & Pavilion www.biquge.info However, among the politicians of the late Han Dynasty, Cao Cao was undoubtedly the one who attached the most importance to science and technology. Seeing the wonder of Cao Chong's imagery this time, Cao Cao became more interested in and attached importance to natural sciences.

Liu Yong was still pondering, Cai Wenji gently pulled his sleeve and said in a low voice: "Brother Liu......"

Liu Yong was stunned and asked, "Miss, what's the matter?" ”

Cai Wenji glanced at Liu Yong, and whispered angrily: "I said don't call me Miss, you can call me by my name or character." ”

Liu Yong teased: "Call you Wen Ji and you don't agree." I think you should think about it, the word Akihime is really not as nice as Bunhime. ”

Cai Wenji's pretty face was stiff, she snorted lightly, and said, "Do you want me to finish speaking, this matter has a lot to do with you." ”

Liu Yong was taken aback, and said busily: "Yes." Yan'er, please speak. ”

Cai Wenji grinned and said in a low voice: "It's rare for the prime minister to be so happy and comfortable today, and the opportunity is not to be given, why don't you go and ask the prime minister quickly." ”

Liu Yong was stunned and said, "What do I have to ask the prime minister?" ”

Cai Wenji raised her eyebrows and said coquettishly: "You pretend not to understand anything." Don't you want to marry Diao? If you ask now, the prime minister will definitely agree to it when he thinks of your careful teaching to Hedge. ”

Liu Yong was moved and helpless when he heard this, he didn't know that this was a good time to ask Cao Cao! But he couldn't. As long as Cao Cao agrees, then he will owe a great favor, which makes Liu Yong, who already loves and respects Cao Cao, in a dilemma, and wants to find an opportunity to leave, how to deal with it, so he has to give up this once-in-a-lifetime opportunity.

"Thank you, Yan'er." Liu Yong had mixed feelings in his heart, and said, "This matter is not urgent, I have my own plans." ”

Cai Wenji hated Liu Yong and said: "If you don't say it today, don't regret it in the future." With that, he turned his head away from him.

Liu Yong sighed, there is still a girl in Wancheng who wants to look at me. Liu Yong, Liu Yong, do you want to be a negative heart?

Two days later, Cao Cao summoned Liu Yong and said, "Chongru, there are a few well-educated people, and I will introduce you to you." As soon as Cao Cao said his name, Liu Yong couldn't help but be taken aback, because these people were all great scientists who were thunderous and famous for future generations, including famous mathematicians and astronomers Liu Hong and Zhao Shuang, and hydraulic scientist and inventor Han Ji......

The water drain invented by Han Ji, that is, the hydraulic blower for iron smelting, greatly improved the problem of low efficiency of human and animal air blasting; Liu Hong is even more remarkable, is a descendant of Liu Xing, the king of the Eastern Han Dynasty, the inventor of the abacus, and was respected by later generations as the "saint of the abacus" and "the father of the abacus" (of course, the abacus at this time was far less than that of later generations). Liu Hong's greatest achievement is in astronomy, he calculated the return year of 365.2462 days, which is not much different from the 365.2422 days measured in modern times, which shows Liu Hong's ability. Liu Hong is seventy years old this year, with gray hair, but he is in good spirits and full of red light; Zhao Shuang, on the other hand, was only eighteen or nine years old, and his body was very thin, but his head was huge, and he looked thoughtful.

"I heard that Mr. is proficient in mathematics, and he is not talented, and I want to learn something, but I don't know if Mr. can teach me." Zhao Shuang bowed his hand and said. He is a few years younger than Liu Yong, so he pays homage as a gentleman.

Liu Yong smiled and said: "Junqing's son is polite, Liu Yong should accompany him." I don't know how Childe is going to compete? ”

"I'll ask the prime minister to come up with the question, calculate it separately, and finally judge the winner according to the correct number and the time it takes?"

"Okay! What does the prime minister think? ”

"Good! This is the verdict for you. Cao Cao looked left and right, Zhao Shuang here was full of ambition and eager to try, and Liu Yong over there was calm and relaxed, not shocked, he couldn't help but smile, thought for a while, and came up with ten addition and multiplication problems.

After a while, Liu Yong and Zhao Shuang handed in the papers successively, and Cao Cao asked Liu Hong and Han Ji to judge together, and Liu Yong was the first. Cao Cao knew this result and didn't think it was strange, but Liu Hong and Han Ji were surprised, just because they knew Zhao Shuang's ability and was the best in the world, and they didn't want to let Liu Yong from a place outside the Western Regions be compared.

Zhao Shuang was not convinced, and asked Cao Cao to increase the difficulty and come up with ten more questions. The clinker results are still the same, and Liu Yong is still the first. Zhao Shuang was a little deflated, bit his lip lightly, and said, "Mr. is so proficient in mathematics, he must know the Pythagorean theorem, right?" ”

"Of course." Liu Yong said with a smile, there is no one who has studied mathematics and does not know the Pythagorean theorem. In simple terms, in a right triangle, the sum of the squares of the two right sides is equal to the square of the hypotenuse. In ancient China, the two right-angled sides were called hook and strand, and the hypotenuse was called the string, so it was called the Pythagorean theorem.

"Do you know how to prove it, sir?" Zhao Shuang's eyes showed a hint of pride. He does have proud capital, although mankind discovered the Pythagorean theorem very early, but it is extremely difficult to prove it scientifically. Zhao Shuang is the first person in the world to be recorded in historical records, and he is the pride of the Chinese.

"Please try to solve it." Liu Yong said respectfully. Liu Yong is not deliberately pretentious, he sincerely admires Zhao Shuang, and he is proud of being a Chinese.

Zhao Shuang took out four right-angled triangles of the same size, put them on the table, and fiddled with them for a while, forming a square with the hypotenuse of the triangle as the side length. Zhao Shuang pointed to the figure and said, "Sir, please take a look." The area of this square is the chord square, right? ”

"Exactly." Liu Yong smiled and cooperated.

"This square is made up of four triangles and a small square in the middle...... Zhao Shuang looked at Liu Yong and continued, "The area of the triangle and the area of the small square are ...... respectively."

After Zhao Shuang finished explaining, he said with a smile: "Sir, what do you think of this proof method?" ”

"Childe's method is also ingenious, and the argumentation process is extremely rigorous and reasonable." Zhao Shuang's face suddenly showed a happy smile, but Liu Yong smiled slightly, and said, "But Son, Liu Yong has a simpler way to prove it." ”

"Huh?" This is Zhao Shuang's most proud work, Liu Hong and Han Ji were taken aback, looked at each other, and couldn't believe it. Zhao Shuang was even more stunned, is there a more ingenious method than me? Zhao Shuang was a little skeptical, but still saluted: "Please also ask Mr. to demonstrate it for Zhao Shuang." Cao Cao also smiled and said, "Chongru, tell me your method." ”

"Yes, Prime Minister!" Liu Yong hugged his fists and bowed to everyone present one by one, took out two of the four triangles in Zhao Shuang's hand, and said with a smile: "Only two are enough." ”

Zhao Shuang was even more stunned, only to see Liu Yong holding the two triangles and putting them together into a right-angled trapezoid. The top and bottom of this trapezoid are the two right-angled sides of the triangle, and the height is the sum of one short right-angled side of the two triangles and the long right-angled side of the other triangle.

If the two right-angled sides of a right-angled triangle are a and b respectively, and the hypotenuse is c, according to Zhao Shuang's method, the area of the large square is c2; It can also be the area of the four triangles plus the area of the small square, i.e., 1/2ab×4+(b-a)(b-a), and after this equation is solved, it is a2+b2, so that c2=a2+b2; Liu Yong's method is like this, trapezoidal area = (upper bottom + lower bottom) × height ÷2, that is, (a+b)×(a+b)÷2, simplification to obtain 1/2(a2+b2)+ab; Again, this trapezoid is composed of three right triangles, and the area can also be expressed as 1/2ab+1/2ab+1/2c2, and comparing the two equations can also give c2=a2+b2.

The two have different paths, although they both use the area method, although they are both equal substitutions, but there is no doubt that Liu Yong's method is simpler. Without waiting for Liu Yong's calculation to be completed, Liu Hong and Han Ji both sighed in their hearts, and Zhao Shuang lost again. Zhao Shuang's face was even more pale, and the work he had devoted himself to studying made Liu Yong easily surpass, and the loss in his heart can be imagined.

Liu Yong saw Zhao Shuang's lonely face, and he couldn't bear it, so he said: "Don't mind, son, the inspiration for Liu Yong's method actually comes from your string diagram." ”

"Is what you said true?" Zhao Shuang was stunned for a moment, surprised and delighted.

"Why should Liu Yong deceive his son." Liu Yong said with a smile, "At that time, when Liu Yong saw Gongzi's string diagram, he felt that this method was extremely ingenious and intuitive, so he thought that it would be better if it could be simpler." Liu Yong racked his brains to come up with this method. In this regard, you can be regarded as Liu Yong's teacher. Liu Yong said sincerely: "Childe, you are the first person in the world to prove the Pythagorean theorem, and Liu Yong admires it very much." As he spoke, he bowed deeply.

"Sir is overrated." Zhao Shuang was happy and ashamed, and hurriedly helped Liu Yong up.

The biggest purpose of Cao Cao's organization of this competition was to use Zhao Shuang and others to suppress Liu Yong. Unexpectedly, after just two rounds of competition, Liu Yong won two games in a row, Cao Cao was suddenly a little disheartened and lost interest, so he said: "Everyone, what is the practical significance of your so-called proofs?" Although Cao Cao attaches great importance to technology, he is not interested in the scientific principles in it, nor does he understand it, what he cares about is the application in production, especially in the military.

Liu Yong suddenly thought of the application examples on the "Island Arithmetic", and said: "Prime Minister, the application of mathematics is everywhere. Liu Yong tried to give an example, for example, to measure the height of Shiren Mountain outside the city, can the prime minister know who can measure it? ”

Cao Cao exclaimed: "The mountain is extremely steep, and it is extremely dangerous to climb...... Cao Cao only knew that to measure the height of the mountain, he needed to ask someone to climb to the top of the mountain, and then put a long rope down, and finally measure the length of the rope. However, unless there is a straight cliff, it will only measure the length of the hypotenuse of the mountain. Since Liu Yong has said so, is it ...... Cao Cao Qi said: "Chongru is a good way? ”

Liu Yong guessed what Cao Cao was thinking, and smiled and said: "Prime Minister, Liu Yong has a simple way to measure it." ”

Cao Cao was happy and suspicious, and asked Zhao Shuang and the others: "Do you have a way?" The three of them looked at each other with a look of shame. Cao Cao had no choice but to say to Liu Yong: "What materials does Chongru need, but do you need to send someone to help?" ”

Liu Yong smiled: "You don't have to be so troublesome, just two wooden poles of the same length." ”

Can you measure the height of a mountain with two wooden sticks? Everyone was amazed and couldn't believe their ears.

Liu Yong smiled slightly, and said in his heart, although you are also great mathematicians, compared to your juniors, Liu Hui, who has not yet been born, your reputation is still a little worse.

Liu Hui was the world's most outstanding mathematician in the third century AD, and he is most famous for two things: one is the invention of circumcision, and he is the first person in the world to find the pi of 3.14; the other is to write the "Nine Chapters of Arithmetic Notes", of which the tenth volume is entitled "Heavy Difference", that is, "Island Arithmetic", which is the earliest work of surveying in China. There are nine questions in the "Island Sutra", all of which are repeated from different positions with a ruler, and the difference obtained is taken to calculate the height of the mountain or the depth of the valley, which is the theory of heavy difference.

The first person in history to discover the theory of gravity difference was Zhao Shuang after middle age, but it was Liu Hui who really used the theory of gravity difference in actual measurement. The so-called gravity difference theory is actually the theory and method of height measurement, telemetry and depth measurement with the help of simple measurement tools such as moments, tables and ropes, and according to the internal relationship between the proportions of the corresponding sides of similar right triangles, realizing the leap from direct measurement (step measurement or measurement) to indirect measurement for the first time in human history. In the field of measurement mathematics, the achievements of the Chinese have surpassed the Western world for about a thousand years, and to this day, the theory and method of gravity difference measurement are still relevant on some occasions.

"Chongru, how about you measure for Lone?"

"The prime minister has an order, but Liu Yong dares to disobey the order?"

Cao Cao was overjoyed when he heard this, anyway, the wooden pole from the last geodesic was still there. Cao Cao immediately dispatched a team of soldiers, with Zhao Shuang, Liu Hong, Han Ji and a group of civil and military generals, to Shiren Mountain. The terrain of Xudu is flat, and after walking for a long time, you can see the peak of Shiren Mountain in the distance. Liu Yong asked Cao Cao to set up camp and set up a seat in the big tent, while he took a group of soldiers to measure.

Liu Yong ordered people to erect a wooden pole about three feet high at a distance of 1,000 paces from each of them, so that the two poles and Shiren Mountain were in the same straight line. Cao Cao saw that Liu Yong was very far away from the mountain, so he began to measure a little hesitantly, and the strategists in the tent also had different opinions, but most of them were suspicious.

I saw Liu Yong start from the first stroke, raise his eyes to look at the clubhead, and then slowly retreat, gradually squatting down, and finally lying on the ground, and finally circled on the ground. When everyone saw it, they didn't know what was going on, and they talked about it for a while. Unbeknownst to them, Liu Yong's move was just to ensure that the peak, the head of the pole, and the points on the ground were in a straight line.

Someone suggested, "Prime Minister, I think we should send someone to measure it on the spot, and it is good to have a comparison with the data measured by Liu Yong, otherwise, how can we know what is right and what is wrong?" ”

Cao Cao nodded, "reasonable", and sent another team of soldiers to measure.

Here, Liu Yong did the same on the second pole, and circled a little more on the ground. Next, measure the distance from the two points to the pole where they are. After a while, Liu Yong took these data back to Cao Cao's big tent and said, "Prime Minister, Liu Yong has finished measuring, and he can calculate and derive the height of the mountain." ”

Cao Cao was dumbfounded and said, "So fast? He exchanged suspicious glances with the ministers and said, "Chongru go and calculate." ”

Everyone here is still arguing, and Liu Yong has already reported the results. Cao Cao saw that everyone was in disbelief and the arguments continued, so he smiled and said: "What is the meaning of the princes' arguments at this time, everyone should be calm and impatient, and they will have their own judgment after the results of the field measurement come out." Let's wait. Cao Cao ordered the soldiers to wrestle in the field, and he and his ministers drank and watched. After half a day, the soldiers who went to measure came back and reported the results, which were almost the same as those measured by Liu Yong. Everyone looked at each other, and the field was suddenly silent.

Cao Cao said with a smile: "Today I have seen the Chongru Divine Technique, which is really mysterious and mysterious." Turning his head and saying to Zhao Shuang and the others: "Lonely and others don't understand the deep meaning, so it's up to you to argue with Liu Yong." Cao Cao was in high spirits and returned to Xudu with everyone.

Liu Yong, Zhao Shuang and the other three were in the same car, knowing that they were still puzzled, so they smiled and said: "The truth in this is actually not profound, and it can be explained in the following small way." The three of them were surprised and delighted, and hurriedly gave gifts and asked for advice.

Liu Yong casually picked up a pair of chopsticks in the car, cut off one of them, and finally left two long, one short and one short. Liu Yong put two wooden sticks on the side of the candlelight, and said: "Everyone, please see, every wooden stick has a shadow, the long shadow is a little longer, and the short shadow is a little shorter, this is a common thing for us." However, I wonder if you are aware of it, what does each stick have to do with its shadow? ”

The three of them observed for a moment, and almost at the same time let out an "ah", and Zhao Shuang was even more surprised: "The ratio of the length of each wooden stick to its shadow is constant. ”

"Exactly!" Liu Yong said, "This is called a similar triangle, and the ratio of the corresponding sides is constant. That's how I measured the height of the mountain......" Liu Yong took another diagram and explained the principle of gravity measurement in detail by schematic diagram. The three of them suddenly opened their mouths and sighed again and again.

"Sir, why don't you measure the height of the mountain by measuring the length of the shadow? Wouldn't it be easier? Zhao Shuang was puzzled for a while, and as soon as the words fell, Zhao Shuang patted his head heavily and said in annoyance, "Look at my stupidity." The shadow of the mountain peak is too long, and it's not good to measure. ”

Han Ji also smiled: "It's not just a matter of the length of the shadow, you also have to make sure that the center point of the mountain peak falling on the ground is not, which is the most difficult thing to do." ”

"What's the hardest thing to do, it's impossible to do at all." Liu Hong stroked his beard and smiled, "Therefore, you can only use Chongru's method." ”

"Actually, the principle of similar triangles doesn't stop there." Liu Yong smiled and said to Zhao Shuang, "Childe, you can also use it to prove the Pythagorean theorem." All you need is a right-angled triangle like this, and you can lead a perpendicular segment from the right-angled vertex to the hypotenuse......"

Zhao Shuang was surprised and delighted, and thought about it. Liu Hong arched his hand and said: "I heard that Liu Gongzi once chatted with the prime minister about literature and geography, and the old man also wants to ask for a question or two, I don't know if it's okay?" ”

Liu Yong hurriedly returned the salute and said, "The old gentleman is polite. Don't hide it from the old man, Liu Yong only knows a little about astronomy and geography. It is just a coincidence that he can answer the question of the prime minister's son, and he doesn't know anything about the zodiac, meridian, solar eclipse, etc., so he doesn't dare to compare with Liu Gong. ”

The three of them were a little surprised to see Liu Yong admit defeat quickly, but seeing that his attitude was sincere, not like a hypocrisy, and they had heard that although he was in a high position, he had a kind temperament and a broad mind, so they couldn't help but feel good. All four of them are people who value science, so they talk happily, and they are still reluctant to give up when they part.

Liu Yong returned home, and the porter said, "Son, there is an old gentleman who has been waiting for you for a long time." (To be continued.) )