I

"There are constant disasters in successive years, which must be felt by heaven and man. Your Majesty said that people help themselves and heaven helps them. This statement is naturally correct, but we must not forget to respect the gods of heaven and earth..."

"The sage said, respect ghosts and gods and keep them at a distance. How can this be explained? It is just like His Majesty, who respects but does not fear. There is an old saying that man will conquer the sky..."

"Datong Monthly" also had a huge influence among scholars.

The most typical manifestation is that civil scholars will also discuss the content of the court meeting published in the newspaper. You know, this is a court meeting. In the past, only the emperor and ministers knew about it. Now ordinary scholars can also see it, so how could they not follow suit?

And no matter how outrageous the dispute is, they are all concerned about state affairs, and they have a sense of satisfaction that they worry about the world.

Hearing the quarrels outside, Chen Zisheng couldn't help shaking his head: "These guys don't do their business, and they follow the country scholars all day long."

Xiao Shixuan said: "Let them discuss it, and it will be quiet after the quarrel."

The planetarium of Qintianyuan is noisy, but the mathematics hall next door is full of crackling and abacus sounds.

"Crack, clap, clap!"

After finishing the abacus, Kuang Hong wrote down the data and said: "The calculation of Huang Zhong in "Historical Records" is indeed wrong, and the value given in "Mengxi Bi Tan" is correct."

"I said earlier that Tai Shi Gong was wrong, but maybe he didn't count it. He made a mistake when he copied the historical materials." Chen Zisheng said.

Xiao Shixuan had a huge calculation in front of him, and he had been working on it for more than half a month, and at this moment he finally came to the result: "Zhu Zaiyu was right, He Chengtian was slightly off."

He Chengtian lived in the Southern and Northern Dynasties, and tried to calculate the twelve equal laws, and got the value: 1.060070671.

Zhu Zaiyu, the patriarch of the Ming Dynasty, also calculated the twelve equal laws, and the obtained value was: 1.059463094.

He Chengtian's calculation method is very rough, and he also used this method to calculate the pi, which was used for reference by Zu Chongzhi when he calculated the pi.

But Zhu Zaiyu was even more ruthless, and made his own 81-level abacus, which could calculate square roots and cube roots with more than 20 digits.

Xiao Shixuan looked at the results of the two mathematicians, pondered their calculation methods, and said with emotion: "Although Zhu Zaiyu's numbers are correct, the mathematical methods he used are too backward. Although He Chengtian is wrong, but His mathematical methods are more advanced. Whether it is Shen Kuo or Zhu Zaiyu, they are not as good as this He Chengtian in terms of mathematical methods!"

Chen Zisheng said: "But Zhu Zaiyu is also very powerful. He also broke away from the traditional three-point profit and loss method, and standardized and revised the Lulu (Twelve Laws)."

Xiao Shixuan said: "Your Majesty taught us the method of analyzing geometry, and we already have the concept of variables. He Chengtian talked about the 'quantity of accumulating micro', and Shen Kuo talked about 'the art of making micro'. Can the combination of the two get the law of twelve equals?" ?”

Chen Zisheng said, "I'm afraid the two have nothing to do with each other."

Xiao Shixuan shook his head: "The shape is not similar, but the spirit is similar. We have to jump out of our thinking and formulate a mathematical method to calculate Lulu. I had this idea two years ago, and I have already figured out something."

Zhao Han's major before time travel did not require advanced mathematics, so he could not teach calculus. But the analytic geometry he taught could serve as a precursor to the invention of calculus.

In fact, Xiao Shixuan has already figured out the differential, and another mathematician has figured out the integral. And they guessed the relationship between differential and integral, but they haven't really demonstrated it yet. They are on the verge of creating calculus, but there is always a layer of window paper that has not been pierced.

Everyone else was kicked out, and Xiao Shixuan was the only one left in the room, quietly facing the super big abacus of one hundred gears.

This kind of super big abacus was invented by Zhu Zaiyu, the king of Zheng, and it comes with a brand new method of using the abacus, which can be used to perform root calculations in a primitive and rough way. For example, to calculate the law of twelve averages, the core problem is to find the 12th root of 2, and Zhu Zaiyu really did it with an abacus.

Standing in front of the abacus from morning to evening, Xiao Shixuan suddenly felt a little hungry.

Integrals and differentials hovered in his mind, as if the two tendons could not be connected, and he walked towards the cafeteria like sleepwalking. Xiao Shixuan didn't know what to eat tonight, he just put the food into his mouth and stared at the table with unfocused eyes.

"Pfft...cough cough cough!"

Xiao Shixuan suddenly thought of something, as if a flash of lightning flashed across his mind. He spit out a mouthful of food, coughed several times, and suddenly ran back to his office.

...

A few days later, Xiao Shixuan asked to see the emperor.

Zhao Han has always treated the researchers of Hanlin Academy and Qintian Academy very preferentially. As long as you have a master's degree or above, you can ask for a meeting at any time, and you must arrange to meet within three days.

"Great mathematician, what new discoveries?" Zhao Han asked with a smile.

Xiao Shixuan said: "Your Majesty, please correct Lulu."

Zhao Han wondered: "It's so good, why do you want to revise the law?"

Xiao Shixuan explained: "Since the pre-Qin period, the twelve rhythms have not been equal. Rites and music are important to the country. Uneven twelve rhythms will be disharmonious when played. Those who study astronomy in the past dynasties know that the yellow bell cannot be restored. For more than 2,000 years, they have been looking for a method to restore the yellow bell. Zhu Zaiyu, king of Xiaozheng in the previous dynasty, has found a method of restoration, and the officials and others have recently verified it, and King Xiaozheng’s calculation is indeed the law of twelve equals.”

Zhao Han became even more confused: "Lulu is music, so why is it related to astronomy?"

Xiao Shixuan said: "The "Book of Changes" is the first of the Hundred Classics. Everything in China in China comes from the "Book of Changes", and the "Book of Changes" comes from astronomical research. The twelve laws correspond to the twelve qi. If you want to count the twelve laws, you must first ask for the Yellow Bell, just like making a calendar to count the winter solstice. The root of the Huangzhong can be used to get the Ruibin, just like making a calendar to calculate the summer solstice. Your Majesty, no matter whether it is a sacrifice or a court meeting, the music played is consistent with astronomy .If you don’t revise the law, it’s like not revising the calendar.”

Huang Zhong is in the key of C in Western music, and Rui Bin is in the key of F # in Western music.

In terms of music, the East and the West are actually the same. For thousands of years, they have been seeking the correct value of the twelve equal temperament, just like everyone is seeking a more accurate pi.

Gong, Shang, Yu, Bianzheng, Zheng, Jiao, and Biangong correspond to the seven white keys of the piano, including Duo Lai Mi Fa Tuo.

The twelve rhythms are also completely corresponding: Huang Zhong (C tune), Lin Zhong (G tune), Taixu (D tune), Nanlu (A tune), Gu Xi (E tune), Ying Zhong (B tune), Rui Bin (F # key), Da Lu (C # key)...

The twelve rhythms are further subdivided. For example, Huang Zhong also distinguishes Qing Huang Zhong, which is the higher octave of Huang Zhong.

The theoretical value of the clear yellow bell should be half of the yellow bell, so that the yellow bell can be restored when the tone is fixed. If the twelve equal temperaments cannot be calculated, the yellow bell cannot be restored, and there must be errors in the temperament. Musicians from both the East and the West have discovered this situation.

Little Zheng Wang Zhu Zaiyu is a BUG. He used an abacus to find the 12th root of 2 without calculus, and forcibly calculated the correct value. This value was spread to the West, and the modern piano was born, as well as the modern music theory system.

Of course, when calculating the twelve equal temperament, music is only a subsidiary meaning, and it can also be applied to many fields such as astronomy.

After Xiao Shixuan explained in detail, Zhao Han finally understood that the music of the East and the West are the same, and that Chinese music is not just a pentatonic scale. The chime bells in the pre-Qin period used twelve rhythms, and the names Huang Zhong, Ying Zhong, and Lin Zhong were probably related to the chime bells in the pre-Qin period.

As for how important the Twelve Lulus are, it can be seen from the "Historical Records" that Sima Qian recorded the data of the Twelve Lulus in detail-although there are still errors in the records.

"Zhou Li", "Book of Rites" and other books also record the twelve laws in detail, but most people can't understand them at all, because they are all related to the numbers of Lulu. Only those who are proficient in mathematics can truly read the "Book of Rites".

Zhao Han said to Li Xiangjun: "Draft an imperial edict and order the Mathematics Museum of Qintian Academy to assist the Ministry of Rites to revise the Lulu. The revised Lulu will be published in the "Datong Monthly News". Revised in Datong Monthly."

"Follow the order."

While Li Xiangjun was drafting the imperial edict, he couldn't help but look at Xiao Shixuan twice more. She studied music since she was a child, but unexpectedly she made a mistake and was corrected by a math student.

Zhao Han asked: "During this period of time, have you verified Zhu Zaiyu's results?"

Xiao Shixuan replied: "Reporting to Your Majesty, not only has it been verified, but also a new set of mathematical methods has been formulated. Zhu Zaiyu used a big abacus to forcibly break the roots. The new method used by the minister is temporarily named 'calculus'."

"Cough cough cough!"

Zhao Han choked and coughed, and made a calm look: "Calculus?"

Xiao Shixuan said: "It is calculus. Xunzi said that the smallest is great, and the one who accumulates the small is the work. The people who study mathematics in later generations, the amount of the small and the technique of making the small are derived from Xunzi's theory. "

In fact, Zhao Han really wanted to say, you are so awesome that you didn't even change your name.

Zhao Han asked: "How did you create the calculus?"

Xiao Shixuan said: "This method benefits from the analytic geometry taught by His Majesty. In the past ten years, with the help of analytic geometry, people who study mathematics have created two sets of methods, which can be called differential and integral. The more they study, the more they discover this The two sets of methods are related. The day before yesterday, I verified the twelve equal laws, and found in the "Sui Shu" the method used by He Chengtian, a scholar of the Southern and Northern Dynasties, when calculating the twelve laws. "But only a few words are recorded. Later, I checked other classics, and I can probably guess what method he used. Although it is not a real calculus, it gave me an inspiration."

"Thank you for your hard work."

Zhao Han can only say that this group of mathematicians actually studies rhythm, but to study rhythm, they have to read "Historical Records" and "Sui Shu", and then get inspiration to create calculus.

What is this all about?

It's too much cross-professional.

Zhao Han thought for a while and said, "Use twelve equal temperaments to invent a musical instrument, and you can play all the melodies by hitting the strings with buttons."

Xiao Shixuan was stunned for a moment, and muttered, "I...no way."

"Forget it, I'll find someone else to make it." Zhao Han thought to himself, you can't do it either, I thought you could invent the piano.

(Thanks to the leader of Joe Jiu for the reward.)