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"Good, good! That old man wants to ask, does Qin Gongzi know the 'Hui rate'? ”

Hearing that Qin Yong agreed to his own request, after a slight pause, Dao Dao Ye quickly asked.

It's just that his opening directly made Qin Yong stunned, and even bystanders like Wu Zixiang didn't know why. Because, the word "Hui rate", that is the first time they have heard it!

In fact, if the "Hui rate" is replaced by the modern language of later generations, it is "pi", that is, π, but in this era, there is no such thing as "pi", and the so-called "pi" is also called "Hui rate" by the world according to its origin.

It turns out that in this era, there have long been various studies on finding the area of a circle, the perimeter, and so on. And in this regard, it is inevitable to involve "pi", because it is a fixed value. So, from the ancient Han Dynasty, there are works on this aspect, and in the Wei and Jin dynasties, the mathematician Liu Hui created the "circumcision", for the calculation of pi to establish a rigorous theory and perfect algorithm, so, this pi, is also called the "Hui rate" by the world.

Of course, Qin Yong came from the later society, and he didn't know what Liu Hui was, so naturally he didn't know that the so-called "pi" was also called "Hui rate", so when he heard the words of Taoism at this time, he would look unclear.

Fortunately, although Qin Yong didn't understand what this "emblem rate" was, but. There are also a lot of people around who don't know, so. And they began to talk about it.

"Ah, Hui rate? That...... What is that? ”

"Huh? You...... Don't you know? It is used when seeking the circle. Know the length of the 'path', and ask for the 'week'. ”

"Oh, that's it! No...... However, this ...... Doesn't seem like an accurate number? ”

"That's right, Jin Liu Hui only asks for three and seven fifty parts!"

……

"Oh? So, they say 'pi'? ”

Qin Yong originally didn't know what the so-called "Hui Rate" was. However, after hearing such discussions from those people, where is it not clear? So, after only half a quarter of an hour, he nodded and answered, "Mr. Dao, here ...... Next. Know a little bit about it. ”

"Oh? It's true? Okay, that's great. In this case, in this third question, it is better to calculate the same problem with you and me, and then see whose 'week' is the most prepared. You...... What do you think? ”

When Dao Zhuye heard Qin Yong say that he actually knew what "Hui Rate" was, he was really overjoyed. Because, this means that Qin Yong does have considerable attainments in the subject of "clear calculation", otherwise. Who would study what "micro-rate" for no reason? Generally, it is rare for people who can know and know this "emblem rate". However, what about Qin Yong? But it's not that you "know a little bit about it". It's "a little bit of understanding", don't underestimate the gap in this one word, because this means that Qin Yong is likely to have studied the so-called "pictograms".

In fact, when it comes to this Cheng dù, although the Taoist teaching is not explicitly stated, Qin Yong has already guessed that the so-called "pictogram" is indeed geometry. Moreover, what they want to study now is the very famous "pi" in later generations. This "pi", in this era, ordinary people really don't know much, but the Taoist teaching is different, he is a great Confucian in the "Ming Arithmetic Subject", so he has almost read through the various "Ming Arithmetic" classics left over from ancient times.

"Count 'weeks'?"

When Qin Yong first heard this term, he was slightly stunned, but soon, he reacted, the so-called "week" should refer to calculating the circumference of a circle, right?

In the modern society of later generations, this is really a simple problem, and probably, it is only in various math exams in junior high school and high school, it will often appear, right?

However, in this era, such a knowledge is not simple, because, in this era, there is no concept of decimal point at all, and the number that should be represented after the decimal point is usually described by fractions, such as "seven out of fifty" that someone on the scene just said. One consequence of this is that when such a fraction is used to participate in the operation with other numbers, the process is even more complicated.

And the calculation of the circumference of a circle, it is precisely because of the complexity of the process that people who are not really focused on academic research like Tao Zhuye basically do not touch it.

Of course, in addition to people who focus on academic research such as Dao Zhuye, many craftsmen and officials in the Ministry of Industry also need to understand a certain amount of "mathematics" and "pictographic" common sense. Because, in this Ministry of Industry, there are many times when you will often use such common sense, for example, when you want to make zuò bronze, ironware, etc., as long as it involves the problem of shape, it will always involve "pictographic" common sense, because if you don't have a certain "pictographic" common sense, then you can't even make a round mirror.

"Yes, then ask Mr. Dao to ask the question!"

Since he knew that he was looking for the circumference of the circle, Qin Yong naturally didn't have any problems. This formula for finding a circle, he had already learned it when he was in junior high school in his early years, isn't it "circumference = pi * diameter"? Therefore, as long as he knows the diameter, he directly substitutes the number into the formula, and it is fine.

"Okay, that's the problem. The 'path' of the old decay is three, and the 'week' is begged. ”

Seeing that it was Qin Yong who agreed to his request, Dao Zhuye quickly said the topic he had thought of in advance.

In fact, this topic was calculated by him not long ago, because, as an authority on the subject of "clear calculation", those officials of the Ministry of Industry also liked to ask him for help.

Actually, isn't that natural? After all, like Zhang Shoucheng, Niu Rongli, and so on, these so-called "geniuses of Gewuxue" who are half a bucket of water. That was also courtesy from the Ministry of Industry, so. Dao taught that he went to the Ministry of Industry, and naturally it also attracted much attention. The main reason why the Taoist Ministry of Industry has recently calculated the circumference of the circle with a diameter of three is because the Ministry of Industry needs to build a circular object according to the emperor's instructions, so the officials of the Ministry of Industry invited the Taoist Department to help.

"If the path is three, it is counted as one hundred and seventy-seven parts of three and one thousand two hundred and fifty. The result should be nine and five hundred and thirty-one parts of two hundred and fifty, and let's see what kind of Cheng dù he can calculate in the end......"

When Qin Yong buried his head in the calculations, this time he didn't do it. Because, he himself has already calculated the final result. The question was just that he wanted to see which number in the "Hui Rate" Qin Yong used.

How many numbers are there in the "Emblem Theory"? Of course, yes, in fact, even in the society of later generations, no one can completely calculate this "emblem rate". Because this is simply an infinite loop of numbers, it can only be as accurate as possible, but it cannot be completely correct. And the Taoist teaching industry is now talking about several "emblem rates". It only refers to the two numbers calculated by Zhang Hui of the Jin Dynasty, that is, 3.14 and 3.1416.

Of course. In this day and age, there is no such thing as a decimal point, so when used as a fraction, it is 157/5o and 3927/125o. As for the origin of these two figures, it is actually related to a method of calculating pi that Zhang Hui of the Jin Dynasty explained. This method is called "circumcision".

The so-called "circumcision" is a method of using the area of the circle connected to the regular polygon to infinitely approximate the area of the circle and obtain the pi from it.

"Yuan, one middle school with the same length". This means that the circle has only one center, and each point on the circumference of the circle is the same distance from the center. As early as the pre-Qin period, the definition of a circle had been given in the Book of Ink, and in the Wei and Jin dynasties, Liu Hui of the Jin Dynasty introduced his method of finding a circle in his mathematical work "Nine Chapters of Arithmetic", that is, "multiplying the radius of half a circle to get the product step", which is basically the formula commonly used to find a circle in later society.

In order to prove this formula, Liu Hui annotated this formula with more than 18oo words in the "Nine Chapters of Arithmetic Notes", and the content of the annotation is also the method of connecting polygons within circles, which is the famous "circumcision" in the history of mathematics.

"Circumcision" only uses the area of the circle to infinitely approximate the area of the circle with the area of the regular polygon, but it is never an infinite number of real polygons, but it just means that the more regular polygons are inscribed, the more infinitely approximate the area of the circle, so when the more edges of the polygon are inscribed, the more accurate the calculated value is.

The two "Hui rates" that Dao Zhuye is talking about today are, in fact, the two situations of different numbers of polygons proposed by Liu Hui in the book, one is the inner 192 polygons, so the final calculated pi is 157/5O, that is, 3.14, and the other is that the 3O72 polygons are inscribed, and the final calculated pi is 3927/125O, that is, 3.1416.

Judging from the above two figures, it is natural that the latter pi is more accurate, but in fact, the "Hui rate" that has been circulating in the market is more of the case of the former one, because, after all, the "Hui rate" in the case of the former is much better, and the "Hui rate" of the 3o72 polygonal is really not something that few people can do, except for a mathematical genius like Liu Hui of the Jin Dynasty.

Especially in this era, because there is no decimal point to save zài, therefore, a qiē calculation needs to be used to the content of the fraction, so it is the case of the front of the 192 polygons, which is already dizzy, not to mention the inner 3o72 polygons in the back, so although the Jin Liu Hui's "Nine Chapters of Arithmetic" has indeed calculated the more accurate number of 3927/125o, but in fact, most people will only put the "Hui rate" It is used as 157/5o, so the result of this is that these people, the area or circumference of the various circles they calculate, are actually not accurate enough.

Of course, such people do not include those who teach the Tao. After all, he is also extremely obsessed with "Ming Arithmetic", so on this issue, he is naturally unwilling to only do the Cheng dù of ordinary people, so when he calculates the circle, he uses the number 3927/125o, and when he was asked to help by the officials of the Ministry of Industry before, he also did the same, so the number he calculated now is more correct than the general situation.

"Is the diameter 3? That would be 3*3.1416, well, the result should be 9.4248......"

Dao Zhuye thought in his heart that the difficulty of such a "seeking a circle" topic should be extremely difficult for Qin Yong, because, even if he knew that the "Hui Rate" was 3927/125o, it would be extremely difficult to calculate it, after all, it involved the problem of scores. Moreover, Qin Yong does not necessarily know that the "Hui Rate" is equivalent to 3927/125O, and it may only know 157/5O, so in this game, he is nine out of ten wins and losers.

However, his point is not here, his real purpose is just to see how high Qin Yong's level is in the "pictogram", so as long as Qin Yong can calculate the circumference of this circle with the "emblem rate" of 157/5o, he is already very satisfied. However, he never expected that Qin Yong not only calculated it, but also calculated it with the same speed.

"Oh? Qin ...... Qin Gongzi, you ...... Are you done? ”

"Huh? 9.4248？ Qin Gongzi, what did you write about? ”

Sure enough, when Qin Yong once again calculated the circumference of this circle in a very short time, the teaching was really speechless, but because of the "experience" of the previous two times, he was not stunned for long this time, so he quickly set his eyes on the answer written by Qin Yong, and the result made him shocked, but quite puzzled.

It turned out that he had already understood the word "9" in front of the decimal point, and he suddenly realized that this answer could really be correct. Because, isn't the answer he calculated for himself also a nine? It's just that it's followed by an extremely complicated score. And what about Qin Yong's now? In addition to "9", there is still a combination of several "Arabic numerals", so the Taoist teaching is very confused, according to his own understanding, this should be a "ninety-four thousand two hundred and forty-eight" extremely large number, but when he thinks that this is the circumference of a circle with a diameter of three zhang, the Taoist teaching industry feels that this is impossible.