Take a plane to the Ming Dynasty

Chapter 167

Chapter 41

Three people pushed the measuring scooter to the podium.

It's not that the measuring scooter is heavy and difficult to push, but out of respect and love for this item, three people are asked to push it.On the contrary, this measuring scooter is not only not heavy, but it is very easy to push.

"Is this the measuring walker?"

"What is a measuring walker?" someone asked.

"You don't know this. It is said that during the Wanli period, Zhang Juzheng, the chief assistant of the cabinet, implemented a whipping method to measure and clean up the land across the country. At that time, farmers used ropes to pull strings when measuring, and then used a ruler to measure the ropes. It was extremely labor-intensive and inaccurate. At that time, Cheng Dawei, who participated in the implementation of a whip method, invented this car, which was called a measuring step car."

Zhu Changyuan also stared at the measuring scooter curiously for a long time, and even ran over to try it himself. It was indeed as he had guessed before, this thing is a large measuring tape.

In my heart, I can't help but secretly admire Cheng Dawei, but I don't have a good impression of Cheng Dawei, this arrogant grandson.

Cheng Shuzheng listened to the comments of the people around him, and he felt very useful. He looked at Zhu Changyuan and said, "If Mr. Zhu doesn't know how to use it, I can measure it for you. It's just, hehe." Looking at the circle drawn by Zhu Changyuan on the blackboard , he did not go on.But the expression has already betrayed his thoughts: You are round, and you are also equipped with my measuring walker?
Unexpectedly, Zhu Changyuan shook his head, and said plainly: "I am here today to teach the art of cutting circles, not to measure the land. You can keep this stuff for yourself."

He walked to the middle of the podium without looking back, and drew an inscribed regular hexagon inside the circle, but what should I say, the drawing of this inscribed regular hexagon is ugly, even the most basic The straight lines are not straight.Naturally, there was a roar of discussion below.

Anyone who understands modern knowledge knows that what Zhu Changyuan drew here is just a schematic diagram.The ancient people didn't understand, so they made a fool of themselves.

"My lords and colleagues, if a perfect circle starts from the center of the circle and connects a line segment to each corner of the regular hexagon, you will find that the inscribed regular hexagon is actually composed of six equilateral triangles. It is easy to conclude that the side length of a regular hexagon is equal to the radius of a circle (I checked it on the Internet, and it was really called radius and diameter in ancient times.)”

What Zhu Changyuan said is the most basic knowledge, among other things, it is recorded in the original geometry, so no one has any objection to this point.

"Okay, this is a consensus, and it is also the basis for cutting circles. Since no one has any objections, I will start the eleventh stage of cutting circles, please pay attention."

When Zhu Changyuan said this, the crowd below who were still a little restless suddenly became silent.

First select one side of the regular hexagon, take out the midpoint, draw a straight line from the center of the circle through the midpoint to intersect the circle, and draw two straight lines from the intersection point to connect with the corners of the nearest two regular hexagons.

So far, there is no difference between Zhu Changyuan and Li Ji's approach, that is, they cut the circle for the first time and cut out one side of the regular dodecagon.

"The basic principle of circle cutting is to gradually expand the regular hexagon inscribed in this circle to become a dodecagon, a 24-gon, a 48-gon, etc. The more sides there are, the more deformed the shape will be. is close to a circle, so the closer its circumference is to the circumference of a circle, the smaller the difference between the two. This is how Zu Chongzhi cut the great circle to the 1th octagon, find Out of the circle the diameter ratio is three one four one five nine two six."

What Zhu Changyuan said now is basically the consensus of these people, so there is no objection from below.

"However, from now on, my circle-cutting technique is different from what you think. The first step of the big circle-cutting technique is to calculate the side length of this dodecagon first."

With a poke of the slate pen, it settled on the side length of the dodecagon on the blackboard.

"This?" Cheng Shuzheng said: "Forget it, what is it for? You can just measure it directly?"

"Yes, we all measure directly. How can we calculate it? Do you think that one plus one equals two?"

"..."

. . . . . .

There was a lot of discussion below, Zhu Changyuan smiled and said loudly: "Okay, since I said it needs to be measured, then I will give you a comparison." He asked in the direction of Xu Ermo: "The other day we cut a large circle with a diameter of thirty feet in your mansion. Tell everyone, what is the length of the side cut out for the first time?"

The side length cut out for the first time is the side length of the regular dodecagon.

When Zhu Changyuan asked, the scene fell silent again.

Xu Ermo happened to bring the data of that day, checked it, and said: "Seven feet, seven inches and six."

"Okay, I'll let you see the difference right now." Zhu Changyuan drew two auxiliary lines on the great circle, and said, "Now, can any master of magic tell me how to calculate this difference using pure calculations? The length of the sides?"

The question is thrown out, how to calculate the side length of the dodecagon according to the side length of the regular hexagon inscribed in the great circle.

Everyone shook their heads.

Some people even said: "How is it possible, this can only be measured, how can it be calculated, it is really a fantasy..."

Even Cheng Buchou, Cheng Shuzheng and his son, Song Yingxing, Huang Mingyu, who are proficient in numerology, are frowning and helpless.

It seems that this is the reason why the ancient people's thinking was rigid, and no one had ever thought about the problem of seeking more and more.This can't be blamed on the ancients, who made Zhu Changyuan such a big cheater?
The tall and thin Song Yingxing stood up from the crowd, cupped his hands and said to Zhu Changyuan: "Master Zhu, Song Yingxing is a Fengxin from Jiangxi, I ask you for advice."

Song Yingxing?
When Zhu Changyuan saw this unremarkable old man, he paid sincere respect from the bottom of his heart, and said, "Master Song, please be polite. Please, Sir Song."

Song Yingxing nodded, pointed at the Dayuan on the blackboard, and said, "Master Zhu, I have thought about this method before. The side length of the dodecagon should be a little more than half of the hexagon, but even if the old man wants to break his head, Never get it right!"

"I dare to ask Mr. Zhu, but have you found a method to calculate the dodecagon?"

Zhu Changyuan said: "Exactly!"

Song Yingxing asked again: "If the old man's prediction is not bad, but the length of the dodecagon is also far from the circumference, so what's the use of Master Zhu calculating it?"

"Good question." Zhu Changyuan said: "This is the essence of the circle cutting technique."

Zhu Changyuan didn't answer Song Yingxing's question directly, he waved his hand to signal him to sit down, and said, "Sir Song, please sit down and tell me, since you thought about it at the beginning, have you ever tried the method of Pythagorean?"

The so-called Pythagorean method is the so-called Pythagorean theorem now, that is, the sum of the squares of two right-angled sides is equal to the square of the hypotenuse.

"Of course I have used it." Song Yingxing just sat down, stood up again, and said: "This question needs to be turned around several times using the Pythagorean method. As I said, from dodecagon to 1 polygons, the old man really has more than enough energy.”

Zhu Changyuan nodded, naturally he understood in his heart.

To calculate the pi accurate to seven digits after the decimal point, you must use the square root operation of eight digits after the decimal point to ensure it.It takes less than ten seconds to use a calculator in modern times, but in ancient times it was necessary to try and add up the numbers a little bit. The work of the month.

This is not a case of miscalculation.

"So, the method of cutting circles that I'm using, might my lord figure it out?" Zhu Changyuan didn't expect Song Yingxing to go so far in the art of cutting circles. If it weren't for the limited calculation conditions in ancient times, it is estimated that this thing can really be restored. .

"Naturally, I can figure it out. The old man thought hard all those years ago and thought that this method is the best way. It's just a pity that the old man can't calculate those data."

"Okay, please sit down." Someone knows his own method, even if only one person understands, it's all right.

Zhu Changyuan looked at Cheng Shuzheng who was sitting in the first row on the left, and asked in the same way: "Master Cheng is also a master of contemporary numerology. I don't know if he can understand the basic principle of cutting circles like this boy?"

Cheng Shuzheng's face turned red. If he didn't understand, he would slap his family and his ancestors in the face, but if he understood, he would slap himself in the face.Because not long ago, he scolded Zhu Changyuan for talking like a chicken and a duck.

"I know a thing or two." After careful consideration, Cheng Shuzheng felt that slapping himself in the face was better than slapping the entire family.

Zhu Changyuan could have taken the opportunity to ridicule, but due to time constraints, he didn't make an inch. Instead, he calmed down, faced the crooked big circle again, and explained to everyone: "Since the circle was cut in Xu's mansion that day, thirty feet was used as a Diameter, today we will calculate the circumference-to-diameter ratio of the [-]-foot circle, please be careful.”

"Let's talk about the principle first, so you have a good idea." Zhu Changyuan pointed directly at Dayuan and said, "This is the radius, which is fifteen feet. This line is half the side length of the hexagon, which is seven feet and five inches."

While talking, mark the data on each line segment.

"Then the next step is very simple. According to the Pythagorean method, the length of this line segment can be calculated." Having said that, Zhu Changyuan paused, looked at the abacus master in the first row, and said, "Masters, please help me." How much is 220 minus the square of seven feet five inches?"

The question Zhu Changyuan asked was very simple, just addition and multiplication.

"Papa papa." Cheng Shuzheng calculated in ten seconds, and said, "It's 160 eight feet seven inches five."

"Prescribe again." Zhu Changyuan said.

Prescribing, huh, huh.

Abacus prescribing is the old Cheng family's specialty. How could it be difficult for this self-righteous master of numerology in front of him. The abacus crackled, and after about 3 minutes, Cheng Shuzheng said: "Twelve feet nine inches nine."

It can be said that this number is already very accurate. The formula of abacus calculation reached two digits after the decimal point.

However, Zhu Changyuan shook his head and said, "Your count is wrong."

"No? Impossible." Cheng Shuzheng almost stood up, checked the calculation again, and said: "Twelve feet nine inches nine times twelve feet nine inches nine, the number is 160 eight feet seven inches four, the difference is only One centimeter, how dare you say that my calculation is wrong?"

(End of this chapter)