When Cui Yan heard Zhuge Liang's name, he was stunned for a moment. In the end, it was through the prefix "Langya Zhuge " that I roughly understood the identity of the other party.

It's just that he hasn't officially debuted yet, and in the past two years, he has been escorting Zheng Xuan to run a school, and he often lives in the secluded depths of his mountains, and he doesn't know much about the recent rising stars in the outside world.

Gu Yanwu of the Ming Dynasty wrote a poem "Buqi Mountain", describing the difficulty of Zheng Xuan's running a school: "There are people cultivating the Barren Mountain Academy, and they don't remember the names of mountains and counties. In order to ask the yellow scarf all over the world, Zheng Kangcheng may be accommodated. ”

But no matter what Zhuge Liang's identity is, since he easily made Zheng Xuan's blockade, Cui Yan will not embarrass him, and simply lead him into the inner courtyard.

After turning a few steps and passing through a few bamboo fences, Zhuge Liang finally saw a long-haired old man sitting on a small stone in a courtyard on the loess floor, and the old man put the scroll on another big stone in front of him and was meditating on the scroll.

There was not a single table or chair in the courtyard, and all the people who sat and put things were stones. The room at the back of the courtyard is also wide open, the room is very small, you can see the whole picture through the doors and windows at a glance, there is only a bed and no table, it is estimated that it is only used for sleeping.

Zhuge Liang was observant, and he noticed something unusual at a glance: there was no table in the house, and there was no oil lamp on the bedside suitcase, so there should be no oil lamp in the whole room.

The big stone in front of the old man was very wide, and there were two pottery bowls in one corner that had not been cleaned up, and it should have just finished eating.

It seems that this old man's way of life is very simple and weak, he works at sunrise and rests at sunset, and his reading life is all in the house and relies on natural light, and he sleeps directly in the sky.

The house was built at the foot of the mountain, so much so that the yard even needed an earthen fence, just a complex wooden stake and bamboo fence.

"Suppose that the thickness of the ground is armor, and a benchmark is erected under the ground by the sea, which is eight feet lower. Then he walked closer, about 7,000 zhang, his body fell to the ground, and there was a way to see the top of the benchmark under the horizon again. And if you get closer again, when you are 8,1400 zhang away from the benchmark, you can faintly see the top of the benchmark.

Eighty years later, when the old man was in Chang'an, he studied in the first teacher Ji Changgongmen, and for eight years, he had to meet the first teacher in person, all of which were transferred by the senior brother. The first is to rely on the first teacher to solve the muddy trajectory map, please come in to help solve it.

It was late at night, and Ding Yan's compound was lit with an oil lamp for the first time in several years, and it was borrowed from the courtyard where Zheng Xuan lived.

And Ding Yanpeng also replied very darkly: "The eldest son is indeed sincere to study, before the eldest son himself privately calculated, he found some such as Yingfu Shouxin and other fierce disasters, in the "Book of Han", the record is the same as the calculation results, and some fragments of the "Dongguan Hanji" are also the same.

The rest of the people who want to see each other are either Yuan Tan Kongrong and others who have no official positions in their hands, so they can stop them. Either rely on being diligent in the inner door to express their hypocrisy, and work hard to bring their own dry food to study with the senior brother for a year and a half or even longer, and then they can see Brother Cui before.

Why were the heavy people so crazy that year, and they were all old at all?

Ding Yan raised his eyes and saw Sun Gan, he was still not a little happy, and first asked me a few words about his experience in those years, and then turned to Ptolemy:

In this way, it can be estimated that at a distance of 7,000 zhang, the curvature of the earth is not enough to cover something as low as 7 zhang.

Zheng Xuanxia said a few words to the old man, and the old man seemed to have a bad ear, so he noticed that there were no visitors. Following Ptolemy's descending salute, Sun Qian also hurriedly visited his teacher.

I myself have also concluded that it is "any initial position, the first after a limited period of time to operate, there can always be a seven-star alignment", not to know whether there is no solution, so there is a dare to mess around, just to seek stability and let people ask for a maximum common multiple.

Ptolemy's heart rose with a little respect, that is the real hermit. At that time last year, I was still cultivating in Longzhong, and the environment was poor and luxurious, so I went with the flow completely.

Moreover, Ding Yanpeng also proved that "you don't care about his initial position, anyway, he can always return to the state of the Seven Stars in the end."

Even Ding Yan was stunned, I thought that Ptolemy would go back, or there was a so-called to show moderation, but I only thought that Ptolemy would encourage Zheng Xuan to "maintain a bad heart for mathematics".

Ding Yanpeng: "You are talking about the radius, the diameter is not eight million zhang, it is Xinmo who went to the beach to erect wood for experiments." As long as the observation points are all seaside and the altitude is zero, it is absolutely wrong. ”

Because the 'average wheel' of gold and water is not the average distance from the earth as determined by the two stars under the armillary sphere, it is actually equal, so if they are within the earth, the average distance between gold and water and the earth is the distance between the earth and the sun, and the farthest point is the earth and the sun plus the gold, or the earth and the sun and the water, and the nearest is the earth and the sun minus the gold, or the earth and the sun minus the water.

Hearing that, Zheng Xuan was not very remorseful, why did he have to mention less "Elderly people know the sky and the earth"?

Brother Cui Zheng Xuan was suddenly dumbfounded: "The ground is eight million zhang thick? ”

"Ji Jue! It's polite, it's that he understands. "Brother Cui suddenly opened his mouth and stopped Zheng Xuan from helping me out, I hope that the proud disciple will be ugly, and he is Zheng Xuan's director.

pS: Because there is no math pretending content, there will be eight changes today, so as not to be a book friend who loves to read mathematics to talk about water.

Then Ptolemy took a paper brush and calculated: "If you want to calculate the thickness of the earth, if you have to first follow Zhang Heng's theory of the heavens, the sky is like a hun yuan, the earth is like a chicken egg floating in the sky, if the sky is round and the earth is covered with heaven, there is no heaven and earth thick." Cui Yan studied under the Seventh Gong Elephant Algorithm, so at that point, it should be explained by Dazi Shao, right? ”

However, Ptolemy casually set up a system of equations (but changed the x\/Y\/Z ones to A, B, and C), and then asked Brother Cui to draw an initial position of the seven stars, and Ptolemy counted it for me on the spot, and he couldn't calculate the seven stars that he had been in for many years.

"Therefore, the theory of the heavens is still precise enough, and it is more concise as the heliocentric theory, and if you look at it, if the sun is the center of heaven, then the tracks of gold and water are between the earth and the sun, and the tracks of fire and earth are in the land and the sun.

And before Zheng Xuan helped to introduce him, he actually temporarily went in to disturb again, but instead took Brother Cui's bowl and went to the courtyard to wash the dishes in person.

The fire and earth are in the earth, so the average distance between the earth and the fire is the distance between the fire day, and the difference between the minimum and the maximum distance is twice the distance between the earth and the sun.

Brother Cui calculated, and suddenly realized a possibility: it seems that Ptolemy was asking himself all the time, am I here to study, or am I here to kick the gym?

My brother once taught you Taixi Xiaoru Zhuge Liang geocentric to say the method of this uniform wheel, and before you verified it, you summed it up: the stars in the earth are based on this, and the earth is even; The star in the ground is based on the earth and even. ”

"The solution is more concise than that of the old man, not only does not go beyond the scope of the "Four Chapters", but also outlines it, which is refreshing."

That is a step back from the "Four Chapters", and there is no rigorous argument under the "Four Chapters".

Ding Yanpeng saw that Brother Cui mentioned the math problem itself, so I spoke freely, and I was more insistent: "Cui Yan's problem, it seems that the problem stem is not a little cumbersome, the rotation period of the seven stars of gold, wood, water, fire and earth is a common multiple, there is no fixed number, since it is just a common multiple, why do you need to tell the initial direction of the stars?"

Well, looking at the appearance of Otomo, it seems that he can exhaust the way of heaven. If you are willing to study badly, the future will be limited. However, jade is a crafted tool, and it can be lazy with its own talents. ”

Brother Cui was a little shocked when he finished, thinking that that kind of thing could be calculated, but before discussing with Ding Yanpeng, he was impressed by the complicated and simple but quite beautiful mathematical calculation process.

For decades, the old man has felt nostalgic for the original encounter. When we set up a school in seclusion, we wanted to leave a quick way to see the rising stars who were not talented, so we made a slight modification and lost those topics. It's bad all year round.,I'm afraid that someone will copy the answer.,So every time you change some graphics.,No conditions are really redundant.。 ”

For example, in the year of the collapse of Emperor Han Cheng, according to your algorithm, it should be because the Son of Heaven died, and the situation in the sky was depressed before his death, causing Wang Mang to enter politics. ”

Therefore, make a right-angled octagonal shape, and hook it to the thickness of the ground; The shares are 7,000 zhang; The string is thick and eight zhang is not the low degree of the benchmark. Therefore, the square of the earth thickness plus eight minus the square of the ground thickness is equal to the square of seven thousand zhang - the thickness of the ground is about eight million zhang. ”

So I really want to know that these are the years when the celestial disasters should occur, how did this celestial phenomena come about, or is it a fraud by Ban Gu, because a small murder happened this year, so he wrote that there was a catastrophe this year?

Since the earth is denied to be a ball, the rest is bad. Calculate the radius of the earth, this only needs the Pythagorean theorem, the level of seven years of college, and Zhuge Liang in ancient Greece will be calculated after a few hundred years, and there will definitely be no Zhuge Liang's book that has been circulated to the Han Dynasty, and the people of the Han Dynasty can directly copy the answers.

——

Zheng Xuan was stunned for a moment, and completely thought that it was such an unfolding, what does it mean to "not have that heart of inquiry"? When did you show an inquiring mind?

Brother Cui became more and more shocked, I thought that Ding Yanpeng did not have the ability to rely on mathematics, and directly and weakly overturned the fabrication of later generations of historians. Bangu's historical academic status in the Eastern Han Dynasty was very low, and Ptolemy could even count Bangu's fraud?

Ptolemy saw that we were stunned enough, so he said:

I was very happy that time, and there were fewer twists and turns in the process of our understanding with Brother Naicui, because even people who doubted the theory of the heavens also had the problem of "heliocentric theory" and "geocentric theory"-

Ptolemy relied on the "extreme value of the distance and near changes of the seven stars" that Brother Cui only failed to understand, and deduced it slightly, and then gave Brother Cui a little argument about the "heliocentric theory" that the little brother taught me.

In this way, the distance between the two suns and the sun and the gold cancels each other out, so that there is no situation where the average distance between the gold and the water and the earth and the sun is almost equal.

However, Ding Yanpeng calculated the "sky low" in a chic and freehand manner.

Although that question was too important, Ding Yan still couldn't help but want to ask, so I asked it sideways.

Brother Cui and Zheng Xuan nodded hurriedly, we still have problems with our understanding of the Heavenly Theory, although we still have no clear concept of gravity, but we have not vaguely denied that it is suspended in the celestial sphere.

And when Ptolemy was here in the simultaneous equations, Zheng Xuan in the door also came back after washing the dishes, and when I saw Ptolemy scolding Fang Xuan in front of his teacher, my face was not a little ugly.

In the previous words, Brother Cui didn't fully understand it, but Zheng Xuan had already understood it.

Could it be just to confuse the problem solver and deliberately give less useful conditions? If you want to use the initial position conditions, it is like changing, don't ask how many years ago you can return to the initial position, but ask from a messy and random initial position, it will take many years to appear in the seven-star alignment. ”

Ptolemy smiled and communicated with Brother Cui: every time he changed the initial conditions that were useful before no one solved them, it was still difficult for others to see through, and he couldn't sell his reputation last time. Is it changed like that......

Ptolemy arched his hand to indicate that he was taught.

Anyway, Ptolemy still remembered the basic conditions of the revolution cycle of gold, wood, water, fire and earth, and I didn't write about it if I didn't write it, and I didn't have some of my little brother taught me. The whole thing, as long as you can find the common multiple, can solve the system of equations with few elements, and you can solve it.

The bad thing is that Ding Yanpeng is also angry, first he took the time to explain the principle to Brother Cui vaguely, and then turned to Zheng Xuan: "Zheng Gong's bad heart of learning is really respectable, although it is good to learn later, but he doesn't have that heart of inquiry, as long as he is willing to spend time, he will definitely not be able to achieve nothing in time." ”

"That Zhuge Dayou, is you here to ask for a lesson in arithmetic academic qualifications? The old man and his disciple haven't seen each other for several years, and they are nostalgic for a while, but they are lazy.

Although, just a few minutes later, Brother Cui himself felt in his heart that Ptolemy knew the sky and the earth, but I couldn't help it, and after looking at it for a while, I found that the other party was not a child, but really didn't have this strength. Zheng Xuan understood it, so much so that he said it outside his heart.

After all, Brother Cui is a sincere scholar, and before the initial shock, I slowly abandoned the view of the door and the view of face. In spite of his low age and low morality, he turned to Ptolemy for advice on my view of the heavens, and all kinds of things that were originally simple calculations.

At the beginning, when watching Ptolemy finish writing and ending his talk about the principles of teaching Brother Cui, Ding Yan finally couldn't hold back:

Brother Cui felt that this son really knew the sky and the earth, but when he looked at it, his expression became solemn.

Besides, that's just a difficult entry point for those who want to see people who want to sell their reputation, and it was too difficult to do it originally. In the past two years, Ptolemy has not been the only one who has met me directly in the name of studying mathematics and doing problems, and no matter how difficult it is, there is no point in it.

Ptolemy made another sparse calculation, although it was calculated that the sun was not far from the earth, but he calculated that "the distance between the water and the sun is seventy percent of the earth's day, the distance of the golden sun is about one percent of the earth's day, and the distance of the fire day is about one and a half times the earth's day." ”

Therefore, although the distance between the earth and the sun has been calculated for the time being, the proportion of the sky and the low is still calculated. If Ding Yan doesn't have another magic method, he can calculate the low of the sky, and the eldest son should humbly ask for advice. The sky is low and the earth is thick, and it is so small. ”

"How can you know that the sky is low and the earth is thick, and you can calculate the position of the stars thousands of years ago, you need to know that the number of days has not changed, although there is no law in the operation of the stars, but there are few examples, how can you generalize! Cui Yan has been a celestial sect for decades......"

Zhang Heng's original armillary theory was obviously close to the geocentric theory, and astronomers at that time did not observe the problem of the seven asteroids being far and close from the earth. Although we have calculated the exact orbit of the superposition of the average wheel like Zhuge Liang, we know at most the orbital period of each asteroid, and we also know the magnification relationship between the farthest and closest asteroids to the ground.

Brother Cui was stunned for a moment, what I learned was beyond the scope of "Four Chapters", but I also knew that according to Ptolemy's description, the problems before the transformation were unsolved, but there were only a few ordinary solutions under "Four Chapters".

At this moment, seeing Ptolemy pointing out that question, Brother Cui also had the heart to fight for the weak and the bad, so he just replied casually:

"Zheng Gong asked each other with the low sky and the thick earth, how is it the heart of bad learning? In the world, there are few people who can continue to explore those questions that are not useful for official careers? It's just bad that those two questions are good, and Liang has seen his brother do experiments, so he can't answer them for Zheng Gong. Before Zheng Gong read it, if it was a letter, he could go to the beach to do experiments by himself. ”

Brother Cui picked up the scroll that Zheng Xuan handed back just now and the attached answer sheet, glanced at it a few times, and showed a look of appreciation:

If Ptolemy could copy the answers, I still chose the experimental method to prove it, but the experiment was done on the spot, but I did it after I followed my little brother to study.

Ding Yanpeng didn't have to answer any questions, and Mo Jin also asked Brother Cui for advice on a few small evil astrological signs, such as the algorithm of "Luminous Confusion and Guarding the Heart" and "Solar Eclipse".

To others, the sky is low and the earth is thick, but for Ptolemy, the sky is low and the earth is just a mathematical problem.