Li Zexuan didn't have any grudges against Guozijian itself, at most, some people in Guozijian didn't like him, and he didn't take these things to heart.

When he resigned in anger, he didn't deliberately target Kong Yingda, on the contrary, during the period when Guozijian was teaching, Kong Yingda took care of him quite a lot, in the final analysis, he was just a little unfamiliar with Guozijian where Confucianism was prevalent!

Besides, it's been so long, and now he just wants to do a good job in Yanhuang Academy, where is the time to entangle those petty grievances?

"Hehe, Mr. Xu, Mr. Liu, come in, please take a seat! Mo Zhong, look at the tea! ”

Mo Zhong welcomed Xu Hongzhi and Liu Hongyuan in, and Li Zexuan hurriedly got up and greeted warmly.

Xu Hongzhi arched his hand and said sincerely: "Mountain Chief, this is Xu's teacher, he has something to ask you for, and I hope you can ignore ......"

"Eh~! Mr. Xu is serious when he says this, this is the first time I have met Dr. Liu, how can I say anything? Come and sit inside, Dr. Liu, please first! ”

Before Xu Hongzhi finished speaking, Li Zexuan interrupted.

Liu Hongyuan glanced at Li Zexuan with great appreciation, and said with a smile as he walked inside with Li Zexuan: "Yong'an Hou is so young and has such a heart, no wonder he can create such a big family business in just a few months!" ”

Several people sat down one after another, and Li Zexuan said with a smile: "Dr. Liu has won the award, you have been working hard in the arithmetic hall for decades, teaching and educating people, and working hard, you are a model for my generation!" ”

Liu Hongyuan is the matter of Xu Hongzhi's teacher, Li Zexuan knows about it, and he has also investigated Liu Hongyuan's previous deeds, this is a respectable "people's teacher"!

Seeing that Li Zexuan's face was kind and there was no displeasure, Xu Hongzhi, who was still a little worried before, suddenly let go of his heart.

At this time, I heard Liu Hongyuan say: "Haha! That's it, that's all in the past, don't mention it again! Today, the old man came to Yong'an Hou, because he had something to ask for! ”

The old gentleman has been teaching all his life, but he has no shelf at all, and his posture is relatively low, which is very different from those rotten Confucians!

Li Zexuan admired it in his heart, and hurriedly said: "Old gentleman, seriously, you have something to say, why don't you ask for anything or not?" Isn't this tormenting the younger generation? ”

Liu Hongyuan listened to Li Zexuan's promise, and he couldn't care about being polite, a trace of blush appeared on his pale old face at this moment, and it was estimated that his heart was very excited at this time, "A few days ago, the old man watched the needle throwing game that Yong'an Hou did you, and in a fit of anger, he also made a similar game in the Arithmetic Museum, and as a result, Yong'an Hou must have heard about it." In his lifetime, he can accurately find the sixth decimal place after the ancestral rate, and the old man is certainly excited in his heart, but ......"

Speaking of this, the old gentleman paused, and Li Zexuan asked out loud very cooperatively, "But what?" Dr. Liu said bluntly that it doesn't matter! ”

Liu Hongyuan nodded, and continued: "But the old man thinks left and right, and he can't think of why he can find the ancestral rate through a simple needle throwing game?" This seems like a bit of a joke! The old man thought about it for four whole days, but he didn't come up with a reason, so he came to the door with a cheeky face, wanting to ask Yong'an Hou for advice, and I hope not to blame the old man for coming uninvited! ”

It turned out to be a needle throwing experiment!

After listening to this, Li Zexuan understood why the old gentleman came, but he couldn't help but feel a little funny, he struggled for four whole days for a problem, this is really a persistent old man!

In fact, many teachers from Yanhuang Academy, including Xu Hongzhi, came to ask him about the principle of the needle throwing experiment, but he didn't say that he wanted the gentleman of the academy to find the answer slowly.

Now that the old gentleman has traveled all the way to this, it is not good for Li Zexuan to continue to sell Guanzi.

"Since Dr. Liu wants to know the principle of this game, then the junior will talk about it today, if there is a mistake, I hope the two of you will correct it~!"

Li Zexuan said politely, and then he took out a pencil from the pencil case on his desk, took a blank piece of paper by the way, and began to explain while drawing:

"Suppose there is a wire bent into a circle so that its diameter is exactly equal to the distance between the parallel lines that I drew on the paper in my previous needle throwing game, and we use d (de) to represent this distance.

As you can imagine, for such a circle, no matter how you throw it, it will have two intersections with parallel lines. Therefore, if the number of times the circle is thrown is n (en), then the total number of intersecting points must be 2n (en). ”

Ahem, people in the Tang Dynasty don't understand English, let alone the reading of English letters, so when Li Zexuan sets up unknown variables, he uses the reading method of Hanyu Pinyin to read it, so as not to be understood by others.

(For the sake of easy reading, the letters will not be marked later)

Liu Hongyuan and Xu Hongzhi both nodded thoughtfully, they had both learned Li Zexuan's new arithmetic, and there were knowledge points about equations in the textbook, so they could also understand Li Zexuan's current practice of setting unknown variables.

Li Zexuan continued: "We now imagine straightening the circle, then the length of the wire is πd, oh, by the way, I generally like to use π to represent the ancestral rate. When the circle is straightened, such a wire that intersects with a parallel line when thrown down is obviously more complicated than a circle, and there may be 4 intersections, 3 intersections, 2 intersections, 1 intersection, or even none.

Since the length of the circle and the straight line are both πd, according to the principle of equal opportunity, when they are thrown more times and equally, the total number of intersections between the two and the parallel line group is roughly the same, that is, when the wire of length πd is thrown n times, the total number of intersections with parallel lines should be roughly 2n.

Now let's talk about the case where the wire is L long. When the number of throws n increases, the total number of intersections m of this wire and parallel lines should be proportional to the length l, so there is: m=kl, where k is the proportionality factor.

In order to find k, it is only necessary to note that for the special case of l=πk, there is m=2n. So k=(2n)/(πd) is obtained. Substituting the previous equation is: m≈(2ln)/(πd) and thus π≈(2ln)/(dm)!

When the length of the line is half the distance between the parallel lines, the above equation can be written as π≈n/m. These are the two pin-throwing games we did earlier! ”

There are some "super-outline" knowledge points in this, and Li Zexuan forgot to explain them as he spoke, and regardless of whether they could understand them or not, he said them all in one go.

Sure enough, Liu Hongyuan and Xu Hongzhi both frowned, and after the two silently "digested" for a long time, Liu Hongyuan asked out loud:

"There is something unclear about the decay, dare to ask what is the principle of equal chance?"

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