Take a plane to the Ming Dynasty

Chapter 168

"Why is Mr. Cheng so excited?" Zhu Changyuan said calmly.

Of course Cheng Shuzheng was excited, this abacus formula is a masterpiece handed down from his family, and no one can get involved in it, so how can this Zhu Changyuan tell him what to do.

"That's right, Lord Zhu." Even Song Yingxing stood up to speak for Cheng Shuzheng, saying: "Mr. Cheng's calculation is not bad, the number of 160 eight feet seven inches five square is twelve feet nine inches nine is not bad... .”

Zhu Changyuan bowed his hands to the audience, and said: "Mr. Cheng also said just now that the number obtained after multiplying this number by itself has a deviation of one percentage point from the original number."

"But Mr. Zhu, the deviation of this one centimeter is very small, and it is so small that it is almost nothing. It can be ignored." Song Yingxing said very reasonable.

The data used in daily life is not accurate to two digits after the decimal point at all, so there is no point in such a dead button.

But Zhu Changyuan shook his head, and said: "I dare not agree with Mr. Song's words. Zhu has a question, and I ask Mr. Song and Mr. Cheng to explain my doubts."

"Tell me." Cheng Shuzheng said with a gloomy expression.

Just now Zhu Changyuan's denial of his abacus prescribing technique is tantamount to denying his grandfather Cheng Dawei's abacus prescribing technique, and it is tantamount to denying his grandfather's achievements in front of everyone. It's no wonder his face looks good. .

"If, I say if." Zhu Changyuan pondered for a moment, thought about the way of expression, and said: "Uh, Liu Hui had already calculated that the ratio of the circumference to the diameter was three and one cent and four centimeters, and Zu Chongzhi calculated three and one cent and four centimeters After that, there is still [-] behind, can it be omitted?"

Everyone was silent.

This time, Zhu Changyuan directly turned to Cheng Shuzheng and said, "If the ratio of the diameter of the circle cut out today is three and one cent three centimeters or three and one cent five centimeters, does it count as a success in cutting the circle?"

Cheng Shuzheng said: "Of course it doesn't count."

Zhu Changyuan asked back: "That's right, Mr. Cheng is so demanding on his subordinates, why is he so unrestrained to himself?"

"This?" Cheng Shuzheng was speechless.

Zhu Changyuan said: "What I'm going to say below is just a small two number, besides, what Zu Chongzhi got back then was a small seven number (seven decimal places after the decimal point)."

"Master Zhu, what you mean is that now all the numbers have to be counted as decimal numbers, and then the ratio of the circumference to the diameter can be calculated?" Song Yingxing's mind turned extremely fast, but unfortunately, basic knowledge and common sense are limited.

Zhu Changyuan continued to shake his head, and said: "We use the decimal number to calculate the circumference diameter ratio, and the final result is only the decimal number that is accurate, because the seventh decimal number is an approximation."

"Oh." Song Yingxing suddenly realized, and said: "My lord means that we must calculate..."

"Little Bashu..." Zhu Changyuan took over the conversation with a smile.

"Little Ba..." Cheng Shuzheng almost spat out a mouthful of old blood after hearing this.

Nima, even if it is an abacus calculation, it takes a long time to calculate a number.

"Hehe." Cheng Shuzheng laughed out loud, and said, "To be honest, the root of the small eight number can be calculated below, but it takes half a day to calculate a number. Such a number?"

Zhu Changyuan counted with his fingers, and said: "Eleven strides, among other things, there are 22 times just to prescribe!"

"Pfft." There seemed to be a black line flying across Cheng Shuzheng's forehead, he snorted twice, and said, "Speaking of which, Mr. Zhu will not be able to calculate pi until next year in today's opening lecture."

Zhu Changyuan sighed sadly and said: "So, I often think about how many years Zu Chongzhi, the master of alchemy, did not have the abacus formula, how many years it took to cut this great art of cutting circles to 280 Octagon? Its heart, wisdom, and perseverance make me admire it."

"On the other hand, these so-called masters today, how can the ancients still have a half-hearted attachment. If there is no such attachment, how can they cut out this ancient thaumaturgy."

After talking for a while, there were admiring gazes from under the stands, and he thought to himself that this is a bit too much to pretend, so enough is enough, he smiled and looked at Cheng Shuzheng, and said: "But today, I won't bother Mr. Cheng to think hard step by step. , I stayed up all day and night for the first few days, and finally calculated all the data before dawn today."

what?
Figured it out.

Naturally, it was calculated. Zhu Changyuan didn't use abacus to calculate the formula. This guy used a calculator and an excel form on the office.

After finishing speaking, use a stone pen to write a large "twelve" neatly on the blackboard, and then, under the twelve, write in small characters: [-].

Eight decimal places after the decimal point, 12.99038106.
"Mr. Cheng, do the math, is it this number?"

The calculation is simpler, just use 12.99038106×12.99038106.

Cheng Shuzheng did the math, and the result was 168.75000008, with very little deviation, almost none.Sighing, he said, "As your lord said, there is almost no deviation."

"Ah, is this really the number?"

"I thought Master Zhu was fooled?"

"Come on, how can Master Zhu be fooled by a dog's eyes? Master Zhu is the man who defeated Huang Taiji and defeated Shenyang Wei. You don't even think about it. Who is Master Zhu?"

"cut."

"Okay!" Looking at the audience who had been shocked beyond measure by him, Zhu Changyuan knew that enough was enough for this pretense, he waved his hand to signal everyone to calm down, and continued to explain: "Okay, find out the length of this line segment Now, you can tell how much this small part is at a glance, just subtract twelve feet nine inches from the radius and [-], that's it."

"Then, use the Pythagorean method again to calculate the multiplication of the side lengths of the dodecagon. Please leave the result to Mr. Cheng."

Cheng Shuzheng did not raise any objections this time, and the abacus was crackling, and within 5 minutes, he calculated a number: 60.28856830.
Zhu Changyuan nodded and said: "That's right, it's the result. Normally, the side length of the dodecagon is after the square root of this number. In order to save time, I actually calculated the square root of this number long ago. Yes, yes..."

Zhu Changyuan reported a number, expressed in a modern way: 7.76457135.
Forget it again?

The others at the scene were fine, Song Yingxing, Cheng Shuzheng, Huang Mingyu and others were really shocked by Zhu Changyuan, and each of them thought to themselves: Didn't this guy calculate all the prescriptions later?

Cheng Shuzheng didn't seem to believe it, and recalculated with the abacus, but the result was shockingly accurate.

"As you can see, the method of cutting a circle we used a ruler to measure in Xu's mansion, we got seven feet seven inches and six; and my method of cutting a circle calculated this number. In fact, where are the following numbers? It can be measured."

"Okay, now there are no doubts. We are calculating the diameter ratio of the first circle cut from the side length of the dodecagon. Mr. Lao Cheng is here."

Cheng Shuzheng crackled again and calculated pi: 12 (number of sides) × 7.76457135 (length of side) / 30 (diameter) = 3.10582854.

(Writing in modern numbers is just to make readers more intuitive. Don’t blame me for saying that ancient people don’t understand Arabic numerals. I know.)
The first step of cutting the circle is to cut the pi to 3.10582854.Of course, this pi is not accurate, because this is the first weight.

Next, is the second layer.

The second step of the circle cutting technique is to cut the regular dodecagon inscribed in the circle into a regular 24-gon inscribed in the circle, and then calculate the 7.76457135-gon from the known side length of the dodecagon 24 The length of the side is used to obtain the ratio of the circumference to the diameter of the second cut of the circle cutting technique.

The calculation method is exactly the same, the only difference is the data.

Since Zhu Changyuan had already calculated all the data needed to prescribe by himself, every time Cheng Shuzheng almost just checked the calculations and told everyone whether Zhu Changyuan's results were correct. Therefore, the speed was faster.

Even so, it took a full 10 minutes from the first heavy cut to the second heavy cut.

The second step of cutting the circle is to obtain the side length of the regular 24-gon inscribed in the circle: 3.91578577.From this, the ratio of the diameter of the second circle is calculated as: 24 (number of sides) × 3.91578577 (length of side) / 30 (diameter) = 3.13262861.

"It's wonderful, it's really wonderful." Song Yingxing deserved to have the quality of a true scientist, after seeing the result of Zhu Changyuan's second round cutting technique, he clapped his hands and laughed, and said, "Master Zhu, Master Zhu, you are truly a genius through the ages. The second step of the circle cutting technique has already yielded three and one cents and three centimeters, the old man is really looking forward to it."

Huang Mingyu sighed, and said: "It's very close, it seems that the old man also underestimated this kid's wisdom before."

Many knowledgeable people at the scene talked a lot, and they were full of praise for Zhu Changyuan's great art of cutting circles.

Although Liu Zunxian, Cao Huachun and Wang Chengen didn't understand, they smiled at each other when they saw so many people agreeing.

"The art of cutting circles, the third level."

Zhu Changyuan's heart was also high-spirited, this pretentious feeling, this sourness, really, f*cking cool.

"The third step of the circle cutting technique is to cut the regular 24-gon inscribed in this great circle into a 48-gon inscribed in a circle. As for the calculation method, it is exactly the same as the previous one."

As he spoke, he continued to draw schematic diagrams on the great circle.

The crooked big circle on the blackboard and the twisted lines on it seem to have infinite magic power, attracting everyone present, including those who don't know how to count, such as Cao Huachun and Wang Chengen.

Now, no one dared to come out and ridicule Zhu Changyuan's circle drawing in person.

Another half an hour passed, and with the help of Mr. Abacus in the first row, I finally calculated the side length of the 48-sided shape: 1.96209388 inches.From this, the third circle diameter ratio is calculated as: 48 (number of sides) × 1.96209388 (length of side) / 30 (diameter) = 3.13935020.

When Zhu Changyuan wrote the calculation results on the blackboard, all the audience at the scene were excited.

"It's one step closer, and now it's almost the same as Liu Hui's three and one cent four centimeters. This, this, approaching again and again, is really an ancient thaumaturgy."

Now, even people who don't know how to count can see that the ratio of the circumference and diameter that Zhu Changyuan cut out is more accurate every time.

If the [-]-fold circle-cutting art is cut to the end, can it really cut out Zu Chongzhi's small seven-number circle-to-diameter ratio?

Many people have such doubts in their hearts.

　Let me say something else before the main text, about the recent chapters.Many readers have reported that the chapters in Beijing are too boring. This old monk does not deny it, but apologizes in advance.Then, after looking at the outline, it seemed that it was not enough, so I decisively cut off about 15 words of pretentious plots such as the plot of treating the disease, the plot of garrisoning the earth and erecting beams, the plot of Qin Tianjian, and the plot of predicting the future.At present, the following twenty chapters are all used for necessary turning points, and they will immediately re-enter the war. Readers are waiting patiently.Due to the need to collect antiques and cultural relics, this chapter on the capital city is essential, a little cumbersome, hehe, no wonder.My old man has changed.Readers, what are you waiting for?Monthly pass, fully booked, rewarded, come here!

　　
　
(End of this chapter)