For the first time in his life, Zhang Fangping felt that his brain was a little short of oxygen: "This is the Great Way! The Great Way is so simple, it can be explained from here! There are so many people who study magic, why has no one ever mentioned this key point?"

Su You smiled and said: "Ming Gong, we will think about this later. Let's solve this problem first. We need to use a few theorems here."

"First of all, we have to prove the vertical diameter theorem and the Pythagorean theorem..."

"Next, we have to prove the similar triangle theorem..."

"Okay, let's connect the highest point of the arc and the starting point of the arc. Now we have two similar triangles, this one, and this one, right? Next, let's set the height from the top to the water surface as the arch, and the diameter of the great circle as the diameter,

The width of the river is a chord."

"Now we have many more conditions. Through these theorems, we can list such a relational formula..."

"This formula can be changed like this...and then like this...Okay, master, can you prescribe alchemy? Yes? Then you can do the calculation."

The master said: "Wait for me to get the calculation chips!"

After a while of maneuvering, the master laughed loudly: "We figured it out! Ming Gong, now we can calculate the diameter of the great circle!"

Zhang Fangping was overjoyed: "Awesome!"

Thinking about it, it didn't make sense: "Wait a minute, I almost got carried away, what's the use of knowing this? Aren't we going to calculate that...arc length?"

Only then did the master come back to his senses: "Yes..."

Su You smiled and said: "If you know the diameter, you can get the circumference through the period rate."

The master nodded repeatedly: "Yes, yes, yes!"

Su You took out another booklet: "This is a table of trigonometric functions. It contains the conversion relationships between right-angled sides of different lengths and corresponding angles. Through it, we can get the angle between arcs."

"The circumference of a circle is one hundred and sixty degrees. You can divide the angle of the arc by three hundred and sixty, and then multiply it by the length of the circle to get the arc length."

The master kept writing: "The arc length is multiplied by the bridge width to get the area of ​​the bridge deck! And then divided by the area of ​​a single stone, you can get the number of stones!"

After finishing the calculation, he threw away the pen and bowed his head in salute: "Young master is really a genius in arithmetic! You can't do anything like Cang Shu!"

Su You held up his hands to Zhang Fangping and said: "Ming Gong, in propositional logic, unproven statements are called conjectures, and conjectures that are judged to be true by reasoning methods can be called theorems. A system composed of countless theorems can be called a theorem.

It is a mathematical system. Geometry is a branch of mathematics. In the final analysis, all content is proved from these simple axioms. This is the essence of mathematics."

Zhang Fangping held his beard in his hand: "This is a wonderful theory! Mingrun, how many theorems have you proved now?"

Su You took out a book from his schoolbag: "This is a new textbook for Wei'er. The children are weak and must be self-reliant, so they need mechanical assistance, and the basis of machinery is mathematics. Dimiao Primary School starts from practicality.

I have achieved some enlightenment, and there are two volumes, each with three volumes, called "Preliminary Arithmetic" and "Preliminary Geometry"."

Zhang Fangping opened it and found some graphics and symbols inside: "Weier, can you understand it too?"

Shi Wei started to complain: "I'm not as smart as Brother Xiaoyou. This book doesn't look difficult, but the question book is weird."

"Many of Brother Xiaoyou's questions require very clever methods to solve. If I can't figure it out, I send it back to him. Brother Xiaoyou will correct it for me with a red pen, and then punish me for doing it five times!"

Zhang Fangping asked: "What about?"

Shi Wei said: "For example, I can add, subtract, multiply and divide, but Brother Xiaoyou said that using three fives and one one, addition, subtraction, multiplication and division can only be used once for each number. In the end, it is very difficult to get the result of twenty-four.

.”

The master suddenly realized: "This is an extended question, just like the last question in the remaining theory..."

Zhang Fangping smiled at Su You and said: "I came from the Accounting Department, and now I am also the Minister of Accounts. I naturally know the importance of mathematics. The Sanskrit numbers you created, the horizontal form, including the accounting books, are indeed simple. Let's try it today.

After trying it, it seems that I really figured it out by myself from simplicity to complexity."

"Back then, I had no one to teach me, so I borrowed books and read them thoroughly to understand things. It's rare, Mingrun, you have the same demeanor as I did when I was a child!"

Su You was frightened: "How dare you? Su You is stupid and Ming Gong has a photographic memory. This is incomparable..."

Zhang Fangping turned to Su Xun and said: "Zizhan Ziyou has a powerful writing style and solid knowledge. I don't need to say anything more. You three, father and son, just prepare for next year's exam."

Su Xun bowed and said: "Next spring, we will come to Chengdu early that morning to prepare for the transportation test."

Zhang Fangping waved his hand: "No, with your talents, you must go to Beijing to take the exam!"

"Ouyang Neihan was a generation of Wenzong, and his disciple Zeng Gong is very close to Dasu Wenwen. I think I will be happy to see you here."

"Although I have different political views with him, we don't have any contact with him on weekdays. When I was the censor, I even criticized the Qingli people for their unsightly actions. Uncle Yong was also very dissatisfied with me."

"However, the atmosphere in the court is still upright now. Our dispute is about state affairs. Each of us has his own insistence and does not harm the way of a gentleman. When it comes to the national selection of talents, I think we all have the same mood, so you must go to Bianjing to participate

Solve the test, make friends with famous intellectuals in Beijing and China, and let your reputation be spread."

"Lao Lei and I are far away from the court, so some things don't require strength, but don't worry, I will definitely entrust you to Uncle Yong and Sheng Yu."

Su Xun felt inexplicable admiration: "Thank you very much, Mr. Ming, for your support."

Zhang Fangping smiled and said: "The matter of a letter is not called support."

He turned his head and looked at Su You up and down: "But this kid, can you stay with me for training?"

What? Su You's eyes widened, am I so destined to be an old man?

"Uh, don't be offended, Mr. Ming, I'm at Meishan Academy..."

Zhang Fangping waved his hand: "I will go to Longshan Chief and tell you that the Chengdu Academy has the original copy of the Thirteen Classics engraved by Shu. Yizhou is not as good as Meishan as a whole, but the teaching level in Chengdu is still good. Why? You look down on me from the third list.

?”

Old man, please stop talking nonsense, Su You is going to pee with fear! You are Song Shou, the "genius in the world" promised by Cai Qi. Who dares to be disrespectful to you, the chosen one who has twice been trained in medical science?!

Speaking of Zhang Fangping's origin, we have to mention the special examination system at that time.

The procedures for the system examination are more cumbersome than the imperial examination. Those who take the system examination are recommended by ministers in the court, usually low-level local officials, or they can be well-known local sages. They then take a preliminary examination, and finally, they are selected by

The emperor himself set the examination questions.

The imperial examinations are held every three years, while the formal examinations are irregular.

The selection is very strict, far more abnormal than the Jinshi test.

First of all, the Renzong Dynasty stipulated that those who participated in the system must be recommended by two ministers.

To get the recommendation quota, you still need to submit your daily opinions and fifty essays to the Hanlin bachelors, Zhizhigao, and Zhongshusheren of the two systems, that is, the internal system and the external system.

After reading Liangzhi, I felt that the boy was excellent in both poetry and theory, so he could be sent to take the pavilion examination.

There are six questions in the secret court test, and every one of them is a stumbling block.

First of all, the scope of the topic is extremely broad, including the Nine Classics, Classics, and Official History.

Don't be busy, that's just the main thing. Next, we have to look at the Seven Books of Martial Arts, that is, the series of military art books issued by the Northern Song Dynasty court as official books: "Sun Tzu's Art of War", "Wu Zi's Art of War", "Six Tao", and "Sima's Law" , "Three Strategies", "Wei Liaozi", "Li Weigong Questions and Answers".

It’s not over, but also includes “Guoyu” and hundreds of schools of thought.

Wait, these are the main texts. How can these alone reflect the quality of our Song Dynasty subjects? Therefore, the annotations written by the great Confucians of the past dynasties for these scriptures are also included in the examination scope...

Taking the exam that Su Shi participated in as an example, the six essays in the exam are as follows:

1. "The King Does Not Rule the Barbarians", source: "Spring and Autumn Gongyang Zhuan", He Xiu's notes;

2. "Who is Liu Kai and Ding Hong?", source: "The Biography of Liu Kai in the Later Han Dynasty", "The Biography of Ding Hong in the Later Han Dynasty";

3. "Rites, Righteousness and Faith Are Sufficient to Become Virtuous", source: "The Analects of Confucius", Bao Xian's annotation;

4. "The situation is not as good as virtue", source: "Historical Records of Wu Qi";

5. "Ritual is based on nourishing people", source: "Hanshu Rites and Music";

6. "Being Drunk and Preparing for Ten Thousand Blessings", sourced from "The Book of Songs Daya Shengmin", annotated by Zheng Xuan.
Chapter completed!