Heng Xun then looked at the picture drawn by Li Zong and said, "I didn't expect that this seemingly irrelevant problem can be solved by using a picture. I think that my friend must have also dabbled in Fang Tian Zhixue."

Li Zong thought about what Fang Tian meant, and then calmly replied: "In fact, I am not only good at calculating Fang Tian, ​​but also like arcs and circles. I am also very good at it. What can I say, relatively regular container volume calculations are all OK."

Heng Xun was also a little surprised and said, "Oh, I wonder if you can tell us all."

Li Zong said: "The younger generation will not hide their weaknesses. If you find that you have something wrong with me, you can raise it immediately."

...

Li Zong will start with the definition.

What is a rectangle?

A rectangle is a quadrilateral with four internal corners equal.

A rectangle can be regarded as countless points, connected into a line segment, and then translated through the line segment, eventually forming such an area of ​​the rectangle.

So what is the area?

Area is the size of the plane figure occupied.

In fact, in this era, there is no such very strict definition at all. Perhaps everyone knows that this is the case, but there is no work to summarize and accurately describe it.

So when Li Zong was explaining, the two suddenly had a strange feeling that they had reviewed the past and learned the new. They clearly felt that they were very familiar with each other, but they also felt that Li Zong was very reasonable.

After talking about the definition, the area formula will come out. The area formula of a rectangle is length multiplied by width.

As for the definition of the formula, Li Zong forgot, he said that this is a formula that applies to any situation under certain conditions, and this is the formula.

Therefore, the area of ​​the rectangle can be written as S=ab in symbols.

Next, Li Zong introduced the meaning of these symbols and once again drew the picture.

After hearing this, although the two thought that Li Zong did this seemed a bit complicated, if you think about it carefully, this is what Li Zong said just now, and under certain conditions, any situation applies.

Ab can be any number, as long as this shape is rectangular, it eliminates the problem of field geometry like in "Nine Chapters of Arithmetic". Many examples need to be given to illustrate the problem of field geometry.

After Li Zong finished talking about the rectangle, his speed gradually accelerated.

square.

triangle.

Parallelogram.

Trapezoidal.

Li Zong expressed everything in symbols, and a picture was combined with a formula. Such a concise way made the two of them scream!

And after passing the trapezoid.

Next...

It's about other graphics that may be a little difficult to understand.

Circular.

sector.

arc.

In order to prove that the area formula of a circle is S=πr2, Li Zong also simply explained that the circle is infinitely subdivided, then cut, and then spliced ​​into a rectangle. As for how to calculate the circumference of a circle here, I believe both of them know how to calculate the circumference of a circle. The circumference of a circle is actually in the process of practice. He was surprised to find that by using wireframes to frame the circumference of a circle of different radii, the conclusion that the circumference is proportional to the radius, that is, the final ratio is almost the same number. Therefore, when it is necessary to calculate the circumference of a circle in the future, everyone will continue to use this number.

It is just because this is the data obtained through experiments, so it is definitely not accurate enough. Therefore, there is a saying that "three-circumference diameter is one", which means that a circle with a circumference of three and a diameter of one. If it is accurate, it means that a circle with a circumference of 3.1415926... has a diameter of one.

Li Zong understood the one with the surname Zhang very quickly, but the old man with the surname Heng seemed to be a little slow.

But Li Zong had such knowledge at such a young age, which was enough to surprise Zhang Gongchuo.

and……

It is even more wonderful that Li Zong deduces from the circumference formula of the circle to the area formula of the circle.

Zhang Gongchuo is the clearest. Although there have been similar records in ancient books, there are no derivation process in ancient books, and only one technique is left.

However, Li Zong invisibly popularized and simplified the "Shu Yue" at this time.

Fortunately, he himself made annotations for Jiuzhang's arithmetic, but compared with Li Zong's easy-to-understand explanation, it is really hard to match.

Heng Xun said: "In the past, I only knew that the half-circumference radius was multiplied to the accumulated steps, but I never understood the meaning. When I saw it today, I realized that it was like this!"

Li Zong smiled and said, "In fact, there are many records about the area of ​​a circle. However, to truly accurately calculate the area of ​​a circle, a difficult problem still needs to be solved, that is, what is π in this formula?"

Zhang Gongchuo raised his fist and said excitedly: "Did you have some research?"

Li Zong said: "This is an incalculable number, so it's enough."

After saying that, Li Zong turned around and stopped talking.

Little did he know that the other party was probably too fascinated, so he tripped directly from the corner of the table, staggered, and fell over, and even pulled Li Zong's clothes tightly, with a full of desire on his face, and asked emotionally, "Did you figure it out? What kind of technique are you using?"

Li Zong was also overwhelmed by this sudden situation, "What are you doing, sir?"

Just a π, you shouldn't be so excited.

"I wonder if my friend has really calculated the pi!"

Li Zong said: "Uh... don't be excited, please say something! Do you know the round-cutting technique?"

In fact, Li Zong didn’t know if there was any circumcision technique in this era.

What if it hasn't come out yet, it's very likely.

Later, I heard Zhang Gongchuo say, "I know this, it is already described in the nine notes of the previous generations."

Just know!

Li Zong then said, "As long as I am willing to keep my feet on the ground and slowly calculate, I can calculate it. Since it was a long time ago when I calculated the pi, the notes were lost long ago, but if I used the symbols I created to calculate, I would definitely be much faster than the calculation. In fact... there are other ways to calculate the pi, but that is too complicated and can't be explained clearly in just a few words, so let's leave it to you later."

But Zhang Gongchuo finally found someone who can calculate pi, so he would let Li Zong go so easily, and quickly said, "I am not afraid of complicated things, just say it."

Li Zong: "Then I'll say it!"
Chapter completed!