The daily life of a peasant girl taking the imperial examination

Hearing Dr. Qin's shocked words, to be honest, Zhuge Yunshu didn't find it strange at all.

After all, this era has been ravaged by war for many years, and many ancient documents have been destroyed.

Even those that were passed down were controlled by those powerful families.

The ancient books and documents available for scholars to read in the Great Xia Library were donated by selfless Confucian scholars or by wealthy merchants for the sake of their reputation.

Thinking this, Zhuge Yunshu bowed respectfully to Dr. Qin:

"I know I am dull-witted, but the reason I was able to solve such a difficult arithmetic problem is because I was fortunate enough to have read the rare mathematical text 'Zhoubi Suanjing' from the Western Han Dynasty..."

The book contains the saying "the circumference of a circle is three times its diameter," the meaning of which is self-evident: it assumes that the circumference of a circle is three times its diameter...

I wonder if Dr. Qin agrees with this viewpoint?

She asked tentatively.

Generally speaking, for a mathematical master like Dr. Qin, there is an almost insatiable thirst for knowledge about arithmetic.

This is precisely why statements like "three Zhou and one Jing" in the Zhoubi Suanjing (周髀算经) are rough values ​​derived from the limited conditions at the time. Once calculated, they will almost always reveal significant problems.

Dr. Qin, instead of answering Zhuge Yunshu's question, asked a question in return:

"Oh, young friend, do you have a disagreement with this statement?"

Pooh!

Old fox.

Despite his complaints, Zhuge Yunshu took out a handwritten book from the cloth bag he carried with him—actually from the "Serving the Country and the People" system—and handed it to Instructor Song.

"The students not only had the privilege of reading the unique copy of the *Zhoubi Suanjing*, but also had the opportunity to read two unique mathematical texts from the Wei, Jin, and Northern and Southern Dynasties period, namely *Nine Chapters on the Mathematical Art* and *Sea Island Mathematical Classic*, written by Liu Hui. One of these texts contains a method for calculating pi called the 'method of exhaustion'..."

As she spoke, she paused, picked up a few sheets of white paper, and found the finest brush. She then drew five or six circles of roughly the same size on the paper.

Thanks to the excellent drawing skills he had honed while drawing maps during this period, everyone could see that the circles Zhuge Yunshu drew on the paper were not only the same size, but also exceptionally round.

After completing this step, she drew a regular hexagon in the first circle.

Wang Yi's eyes lit up when she saw this.

She now understood Zhuge Yunshu's intention in doing so.

I wanted to take this opportunity to prove to them that the circumference of a circle is not a precise value such as three times its diameter.

In addition, these women were fortunate enough to witness the calculation of pi.

Thinking this way, how could Wang Yi not be excited?

However, Sun Wenxiu of Xiaoshan County shared the same idea as her.

At this moment, he looked at Zhuge Yunshu with a shocked expression.

You must understand that in their Great Xia Kingdom, the major aristocratic families, for the long-term development of their clans, and even for the sake of their descendants' reputation, would generally keep such rare books hidden away and only pass them on to their direct descendants...

What's more, it's done in such a public way, in front of so many people, to explain it in detail to everyone.

What is she after?

Sun Wenxiu murmured softly.

Dr. Qin's expression was also not good at this moment.

He had originally planned to find a way to 'borrow' the two rare arithmetic books in Master Wang's possession after the competition.

But who could have imagined it?

This young boy, with his unborn child, was thus brazenly displayed before everyone.

"That's such a waste!"

Dr. Qin felt a sharp, throbbing pain in his heart.

If he were given this rare copy, he would surely make the most of it.

Heartache is heartache.

Dr. Qin also kept a close eye on what Zhuge Yunshu was doing.

At this point, Zhuge Yunshu had progressed from drawing regular hexagons in circles to drawing regular 24-sided polygons.

Wang Yi and Zhang Hao, with their keen observation skills, helped her measure the side lengths of the regular hexagon and the regular dodecagon within the circle, and recorded them one by one.

It was at this moment that Wang Yi was surprised to discover that the more sides a regular polygon inside a circle has, the closer it is to a circle. Moreover, its perimeter is closer to the circumference of a circle.

Although calculating the perimeter of these regular polygons is quite complicated, Zhuge Yunshu, who came prepared, taught Wang Yi and Zhang Hao a relatively systematic algorithm.

Then, by dividing the circumference of the circle by its diameter, we eventually obtained a value that kept getting closer and closer to the correct value.

Pi is between 3 and 3.

Of course, in order to obtain this result, Zhuge Yunshu repeatedly calculated within the system for serving the country and the people for several days.

The reason she got the result so quickly today is because she was already familiar with the process...

However, despite the astonishment of everyone in the training ground, Zhuge Yunshu spoke with unusual composure:

"This is how Liu Hui of the Northern and Southern Dynasties calculated pi using the 'method of exhaustion'. The final result was derived by later generations based on his method..."

Therefore, if you encounter similar mathematical problems in the future, just remember this value, and you will get the closest result to the correct answer.

At this point, she glanced at the students who were quickly writing numbers with calligraphy brushes and reminded them:

"These are only approximate figures. If you want to get a more accurate answer, you will need to work harder in the future."

After all, pi is an infinite non-repeating decimal, even with the supercomputing power of modern supercomputers.

Thinking this, Zhuge Yunshu shook his head helplessly.

Why is she making things so complicated?

So, while everyone in the training ground, especially Dr. Qin and Sun Wenxiu, was still in shock at this number, Master Wang dropped another bombshell:

"The handwritten book in Brother Song's hand is a copy of 'New Collection of Arithmetic Commentary' compiled by Yun Shu based on three rare mathematical texts: 'Zhoubi Suanjing', 'Nine Chapters on the Mathematical Art', and 'Sea Island Mathematical Classic'..."

It not only preserves the original annotations left by our predecessors, but also includes some new insights from Yun Shu, especially regarding the problem-solving process, which is simpler and easier to understand than before...

He paused for a moment as he said this.

"This copy of *New Collection of Arithmetic Commentary*, along with three unique mathematical texts—*Zhoubi Suanjing*, *Nine Chapters on the Mathematical Art*, and *Sea Island Mathematical Classic*—will be donated to the Linxi County School in the name of the Yunshui Town School for a one-year pilot program, after which they will be donated to all official schools under the jurisdiction of Pingchuan Prefecture..."

Three years later, it was donated to the Great Xia Library for everyone to read.

As soon as he finished speaking, the training ground erupted in an uproar.

In particular, Instructor Song felt as if a huge pie had fallen from the sky and landed right in his arms.

Such joy cannot be expressed in words.

He could only tremble and bow solemnly to Master Wang and Zhuge Yunshu:

"Having received this work on mathematics, I have no way to repay you, so I can only offer this token of my gratitude... Thank you for your generosity, Brother Wang and young friend Yun Shu."

As soon as he finished speaking, all the students of Linxi County School in the training ground stood up:

"Many thanks to Master Wang and Junior Sister Yun Shu for their generosity."

The powerful sound drew applause and cheers from the crowds watching the spectacle around the training ground.

Faced with this remarkable feat, Dr. Qin and the twelve students from Xiaoshan County School all stood there with embarrassed expressions.

Dr. Qin, in particular, felt that Master Wang, the headmaster of Yunshui Town School, was definitely targeting them on purpose.

The donation was first given to the county school of Linxi County, then to all the official schools under Pingchuan Prefecture, and finally to the Great Xia Library. Five or six years have passed in this manner.

The meaning is self-evident: they want all the official schools under the jurisdiction of Xiaoshan County to be the last to receive the education.

Thinking about this, he could already guess how those literati in Xiaoshan County would use their pens to criticize him in the future.