It seems that Ge Dongzan is planning to hold on to the end for the sake of face, and resolutely does not ask Li Hao for answers, wants answers, and thinks slowly after returning to Tibet, he doesn't believe it, with his own ingenuity, as long as he is given enough time, he will not be able to think of a way to solve this problem.

At this time, Li Tai on the side suddenly scratched his head like crazy and screamed anxiously, everyone was startled, and turned their heads to look at Li Tai, Li Hao saw Li Tai's appearance, and knew that he was forced to be like this by the question he had just asked, no wonder he didn't ask for an answer just now, because he had been thinking about the problem, and he really forgot about it.

"Li Hao! What is the answer! Li Tai finally stopped scratching his head and stopped screaming, and then looked at Li Hao with wide eyes.

Li Hao was stunned when he heard this, glanced at Li Tai, and then turned his head to look at Lu Dongzan, Lu Dongzan sneered all over his face, as if to say, "This is not what I asked." ”

Li Hao thought for a while, and finally shook his head and said: "This question is for the Tubo minister, only the Tubo minister can ask for the answer." ”

"What!" Li Tai was stunned for a moment when he heard this, and immediately came to Lu Dongzan, saluted and said, "Senior minister, in order to solve the confusion in the hearts of the juniors, please ask the seniors to help the juniors and ask Li Hao for answers." ”

Lu Dongzan returned the salute and shook his head apologetically: "His Royal Highness the King of Wei is serious, please forgive Ge Dongzan for being difficult to obey." ”

Li Tai was disappointed when he heard this, and just wanted to turn his head and walk back, but suddenly a flash of inspiration flashed in his mind, and he suddenly bent down to Lu Dongzan's ear and whispered: "As long as the minister helps the king find an answer, the king can help the minister marry a princess of the Tang Dynasty and return to China." ”

Lu Dongzan was shocked when he heard this, looked at Li Tai with wide eyes and disbelief, and asked, "Is this true?" ”

"Naturally, take it seriously!" Li Tai replied seriously.

Lu Dongzan believed that Li Tai was the dignified King of Wei and should not lie and deceive people, so he almost did not hesitate to bow his hand to Li Hao and said, "Li Xianhou, please tell me the answer to the question just now." ”

Li Hao was slightly surprised when he heard this, and he didn't know what Li Tai said in Lu Dongzan's ear, which could make Lu Dongzan's attitude change 180 degrees in an instant, but since Lu Dongzan asked for the answer, he couldn't help but say it, so he said: "Please return the pen to me." ”

Lu Dongzan returned the pen to Li Hao, and Li Hao turned his head to Li Shimin and said: "Your Majesty, Weichen still wants to ask for a ruler, but it is not an ordinary ruler, but a triangular ruler used by carpenters." ”

Li Shimin also wanted to know the answer, and immediately said in a loud voice: "Come on, go to the Ministry of Industry to get a triangular ruler." ”

Immediately, Jin Wuwei took the order and left.

Everyone in the hall waited boredly, and Li Tai, the king of Wei, simply sat on the ground next to Li Hao and Lu Dongzan, waiting for the answer, he wanted to see Li Hao find the point to open a dock by the river.

After a long time, Jin Wuwei panted and sent a triangular ruler over, Li Hao took the triangular ruler and looked at it, very satisfied, and then began to solve the map.

Li Hao first overlapped a right-angled side of the triangular ruler with the south edge of the river, and then pushed horizontally until the other right-angled edge coincided with the Li family, and then drew a dotted line along the right-angled edge with a brush, which started from the Li family, connected to the river, and perpendicular to the river.

Li Tai hurriedly asked: "This is the first way?" ”

"It's not." Li Hao shook his head and said, "This is an auxiliary line, which is used to help solve problems." ”

Although Li Tai had never heard of the word auxiliary line, as soon as he heard the name and Li Hao's explanation, he instantly understood what an auxiliary line was.

Next, Li Hao extended the auxiliary line to the north, and it was still a dotted line.

Lu Dongzan and Li Tai were beside him, and they saw it very clearly, looking at Li Hao without blinking, until this moment, they still didn't understand why Li Hao wanted to draw this auxiliary line.

Then, Li Hao measured the length of the dotted line from Li's house to the south bank of the river, which is actually the shortest distance from Li's house to the river, exactly four inches, so he took the intersection of the dotted line and the south bank of the river as the starting point, measured the length of four inches in the direction of the dotted line to the north, and drew a big black dot on the four inches, and marked the text next to the black dot - "Muzi".

Seeing this black dot and the word "Muzi", Li Tai's heart was full of doubts, but the point and route of the pier did not come out, so he could only endure it and wait for Li Hao to continue to solve the problem.

Next, Li Hao used a ruler to assist in connecting the "Muzi" black dot and the Wangjia circle into a line, and at the intersection of this line and the south bank of the river, Li Hao wrote two words - "wharf"!

Li Tai and Lu Dongzan were shocked when they saw it, and the dock was pointed!

Li Hao drew a straight line between the dock point and the Li family, and the dock and the two roads have all come out, and the problem is solved.

Li Hao picked up the drawn picture, showed it to everyone, and said loudly: "This is the correct answer." ”

Everyone stared wide-eyed, although the dock point and the two routes were drawn on the map, but they still didn't understand what the truth was, Li Shimin coughed lightly twice, and said, "Submit it, let me take a look." ”

Xu Lian came to Li Hao, took the picture, and presented it to Li Shimin, who stared at the picture for a long time, but didn't see why.

Li Tai and Lu Dongzan were both frowning and pondering, they also felt that Li Hao's answer was correct, but they couldn't say what the principle was, it was like a cat's claw scratching their hearts, it was really painful.

After a while, Lu Dongzan couldn't help it anymore and asked, "Li Xianhou, I feel that your answer is correct, can you explain the reason why you are looking for the dock point." ”

"Yes!" Li Tai also shouted anxiously, "Why did you draw an auxiliary line and draw a black dot called 'Muzi'?" ”

"You two please get up first." Li Hao said and slowly got up, and Lu Dongzan and Li Tai also stood up.

Why did Li Hao call them to get up at this time, because ...... His feet were numb.

Li Hao stomped his numb right leg lightly, and after a while, he finally regained consciousness, and then he smiled awkwardly and said, "Actually, the key to solving this problem is 'between two points, the straight line is the shortest'." ”

There is a basic saying in geometry that "between bright spots, the line segment is the shortest". Because in geometry, straight lines are infinitely long, so for the sake of scientific standardization, it is said that the line segment is the shortest, not the shortest straight line, but the people of this era do not know what a line segment is, and Li Hao is too lazy to explain to them what a line segment is, so he can only say that the straight line is the shortest.

Everyone nodded when they heard this, indeed, between two points, it is indeed the shortest straight line.

Li Hao then said: "The Li family and the Wang family are regarded as two points, and they cannot be directly connected with each other, because they do not meet the requirements, the requirement is to set up a wharf by the river, and the wharf is also a point, then it is three points, how to make the connection between these three points the shortest, then, only let these three points be in a straight line." ”

Li Tai and Lu Dongzan continued to nod, these truths seemed simple, but they didn't even think about it when they thought about it.

Li Hao continued to explain: "But you have also seen that the Li family and the Wang family are fixed points, and the wharf is a point that can be moved, but although the wharf can be moved, there are also restrictions, and it must be by the river, to be precise, on the south bank of the river. I don't know if you have noticed that the Muzi point and the Li family are actually symmetrical, and the axis of symmetry is the Henan shoreline. ”

Li Shimin flipped the picture according to Li Hao's words, and suddenly, there was a low cry from the crowd, and sure enough, the dotted line between the two points of the Li family and Muzi was perpendicular to Henan, and it was as far away from the south bank of the river, which was axisymmetrical.

Li Hao said: "This method, also known as the mirror map, is like a mirror reflecting things, the picture that is reflected, although they are all virtual images, but the size and size are exactly the same as the original, but the direction is the opposite, so the wooden point is actually the virtual image of the Li family on the north bank of the river, and the reason why such a virtual image is set up is to make the three points on the same straight line." ”

Li Tai and Lu Dongzan are both smart people, and when they heard this, they finally realized that they carefully checked it, and sure enough, they found that the line between Muzi Point and the wharf and the line between the Li family and the wharf were also axisymmetric, that is, the length was also the same.

Many ministers were still confused at the moment, saying that they didn't understand, Li Hao thought about it, and suddenly said: "Your Majesty, please fold the paper along the line of the south bank of the river." ”

Li Shimin heard what he said, the paper was very thin, when Li Shimin lifted it up, everyone exclaimed, only to see that the folded paper could still vaguely see the picture inside, the two points of the Li family and Muzi overlapped together in an instant, and now, the ministers finally understood.

Lu Dongzan had to accept this time, and arched his hand towards Li Hao and said: "Li County Hou Zhizhi, Ge Erdongzan is far behind." ”

Li Hao bowed his hand and said: "It's ridiculous, in fact, when I first saw this question, I didn't come up with an answer." Li Hao told the truth, when he was in junior high school, just came into contact with geometry, the math teacher gave them such a problem, the whole class was confused, no one came up with the answer, and then the math teacher told the way to solve the problem, and finally in order to tell them a truth - "between two points, the line segment is the shortest".

"Alright." Li Shimin was very happy, and said with a red face, "Since this battle of wits in front of the palace was won by Li Hao, the Marquis of Lantian County, then I will marry Princess Wencheng to Li Hao, however, Princess Wencheng is the daughter of the clan, because she wants to marry Tubo, she will be specially named the princess, and I will issue a decree tomorrow to remove the title of Princess Li Ping Wencheng, the daughter of the clan, and give Li Hao to marry, and choose a good day and an auspicious day to complete the marriage!" ”

Lu Dongzan was slightly stunned when he heard this, it turned out that Princess Wencheng was not the daughter of the emperor, but now he didn't care, because he lost, he couldn't help Songtsan Gampo marry Princess Wencheng back to Tibet, besides, Songtsan Gampo wanted to marry Princess Datang, as long as he had the title of princess, it didn't matter whether it was Li Shimin's daughter or not.

Lu Dongzan slowly turned his head to look at Li Tai and said in a low voice, "Your Royal Highness King Wei, don't forget your promise. ”

Li Hao on the side was stunned when he heard this: "Promise? What promises? What did Li Tai promise him just now? ”

Li Tai smiled indifferently and replied in a low voice: "This king will fulfill his promise now." ”