Imperial Master of the Ming Dynasty

The emotional atmosphere has reached this point, and it is obvious that the discussion group will not stop until the sun is measured.

Zheng He enthusiastically held his long beard and asked.

"So, how can we measure the distance between us and the sun?"

Jiang Xinghuo did not answer the question directly. He glanced at the other person's neck that was exposed because he was holding his beard and said, "Do you know the Pythagorean Theorem?"

As a child who grew up in a cultural desert, Zhu Gaoxu coughed awkwardly.

Although Old Man Zhuo couldn't stand Zhu Di, Yan Ni, who rebelled and killed the king, he didn't seem to have any special objections to Zhu Gaoxu.

I guess I think everyone has their own master?

Or do you disdain to argue with your juniors?

Anyway, Zhuo Jing still solved Zhu Gaoxu's confusion.

"The "Zhou Bi Suan Jing" once recorded a conversation between Shang Gao and the Duke of Zhou. Shang Gao said: ... Therefore, when breaking the moment, gou Guang three, Gu Xiu four, and Jingyu five. This is the origin of the Pythagorean theorem. "

That is to say, when the two right-angled sides of a right triangle are 3 (hook) and 4 (strand) respectively, the corner (string) is 5. People in later generations simply said this theorem as "hook three strands and four strings" Five", according to this allusion, the Pythagorean theorem is also called the Shanggao theorem.

Zhao Shuang of the Three Kingdoms era made a detailed explanation of the Pythagorean theorem in "Zhou Bi Suan Jing". It was recorded in "Nine Chapters of Arithmetic" that "the Pythagorean theorem is multiplied by each, combined and divided by the square root, which is the string." Created by Zhao Shuang Drawing a "Pythagorean Circle and Square Diagram", using the method of combining numbers and shapes, a detailed proof of the Pythagorean Theorem was given.

"It doesn't sound too difficult." Zhu Gaoxu commented.

Jiang Xinghuo said calmly.

"It's not difficult. I didn't say how difficult it is to measure the sun."

"Hiss~"

In Jiang Xinghuo's view, it is true that a series of calculation processes that future generations of junior high school students can figure out in mathematics and physics are not that difficult.

After all, your predecessors have already told you how to operate it, you just need to follow it. You are not asked to invent the torsion scale experiment or the ball throwing experiment from a high tower, nor do you need to understand "Why Pan Jinlian's bamboo pole fell on Ximen Qing" head instead of flying into Chang'e's hand."

But for the people of Ming Dynasty.

This calculation method, which can be said to be "picking the sun and moon by hand", is obviously too advanced.

"Then what does the Pythagorean Theorem have to do with measuring the distance between us and the sun?"

As Jiang Xinghuo's first disciple, Zhu Gaoxu knew his inherent impression in Mr. Jiang's mind, so he gave full play to his excellent academic style of asking questions when he didn't understand.

"It does matter."

Jiang Xinghuo continued to draw.

No way, geometry is really useful sometimes.

Moon————Sun

丨

Earth

Jiang Xinghuo said: "Let me tell you an important prerequisite first, that is, the moon itself does not emit light. The moon's light is reflected from the sun."

After that, Jiang Xinghuo took out his classic teaching aids again.

The Pasiba silver coin left to him by Li Jinglong.

"moon."

The young and old looked at each other.

"oh"

Referring to a deer as a horse is a yes.

But seeing the silver coin pointing at the sun and starting to reflect light, the three of them understood what Jiang Xinghuo meant.

"Then let me ask you, when will the moon, sun, and earth be like the picture drawn above, with the moon as a point, in a straight line with the sun and the earth at the same time, forming a right angle?"

Jiang Xinghuo fiddled with the silver coins in his hand and adjusted its position.

Looking at Jiang Xinghuo's movements, old man Zhuo, who was twirling his beard, reluctantly pinched off a beard because he was too excited.

"When the moon is crescent!"

"That's right."

The so-called quarter moon is divided into first quarter moon and last quarter moon. This is because the positions of the sun, earth, and moon are constantly changing, and the moon phases will change in gain and loss. The ancients were also fully aware of this, so they included the calculation of the day. Regarding eclipses, lunar eclipses, etc., the Ming Dynasty followed the Yuan Dynasty's "Time Calendar" and was able to get it right seven or eight times out of ten.

Oh, by the way, there is another point that ordinary people can easily overlook.

One month, why is it called a "month"?

This is because the part of the moon facing the earth that is illuminated by the sun gradually increases from new moon to full moon, and the moon phase changes from waning to waxing. The replacement cycle of the moon phase is 29.53 days, which is approximately equal to 30 days.

30 days is a "month".

Back to the topic, the so-called waxing and waning moon, judged from the moon phase, the complete edge arc of the moon that can still be seen is used as the bow arm, and then a dotted line is made to connect the two ends of the arc, and it is imagined as a bow string. The string is on the upper side of the moon. The moon, on the lower side, is the waning moon.

That is, a ○ is cut in half diagonally from northeast to southwest or vice versa, which is the shape of a waxing and waning moon.

Whether it is the first quarter moon or the last quarter moon, the moon is evenly cut in half.

In other words, the sunlight reflected on the surface of the moon is at a right angle to the earth!

It was precisely because he understood this truth that Old Man Zhuo excitedly pinched off a precious and few remaining beard.

Old Man Zhuo said with great interest, pointing to the earth, moon and sun painted on the ground.

"As long as it is a quarter moon, you can get a right angle according to the hours and moments calculated by the Qin Tianjian of the past dynasties. As long as you get the right angle, and then calculate the angle between the earth and the sun, you can get the two angles of the triangle, and the third Three angles, just need to reduce it and it will come out!”

Old Man Zhuo became more and more excited as he talked, and even began to dance a little.

"And the angles of the three angles of the triangle have been calculated. Assuming that the distance between the earth and the moon is unit one, then the distance between the earth and the sun and the distance between the moon and the sun can also be calculated, and then, then."

Old Man Zhuo's eyes began to become a little confused.

The Pythagorean Theorem can only derive three sides and three angles. There is no way out!

"Then what's the calculation?"

Jiang Xinghuo reminded: "Based on the diameter of the earth, calculate the diameter of the moon, and then deduce the diameter of the sun."

"How to calculate?"

Jiang Xinghuo started drawing on the ground again. As he drew, he said: "The Pythagorean theorem calculates the distance ratios (assuming the distance between the earth and the moon is 1 unit) and angles between the earth, the moon, and the sun. Then we can use the equation Scale it up to calculate the diameter of the sun."

Earth - Moon - Sun

After finishing the painting, Jiang Xinghuo explained the principle.

"Because when the three are aligned, that is, during a total solar eclipse, the moon can almost perfectly block the sun."

"Then when viewed from the earth, the size of the sun and the moon are basically the same, which means that the angle of view of the moon and the sun from the earth is the same. So, since the Pythagorean theorem knows that the distance from the sun to the earth is approximately the distance from the moon to the earth Then we can also estimate how many times the diameter of the sun is the diameter of the moon using a very basic proportional relationship between similar triangles."

Seeing that the eldest disciple didn't understand, Jiang Xinghuo directly drew two triangles next to each other, and then enlarged the second one in equal proportions. Only then did Zhu Gaoxu understand.

"So next, because Guo Shoujing has already calculated the radius and diameter of the earth, we only need to calculate the ratio of the diameter of the earth to the moon. After getting the diameter of the moon, we can calculate the diameter of the sun in the previous step by inverting?"

Old Man Zhuo reacted.

"exactly."

Jiang Xinghuo nodded in agreement, and then said: "Then think about it, how do you calculate the ratio of the diameter of the earth to the moon?"

——————

"How to calculate the ratio of the diameter of the earth to the moon?"

In the secret room, Zhu Gaochi started to engage in "three bad generals against Zhuge Liang", and he looked at Guo Jing and Chai Che.

Not to mention, brainstorming is much better than thinking hard alone.

"Your Highness, I have an idea," Chai Che said suddenly.

"Come and listen."

Zhu Gaochi said hurriedly.

"Mr. Jiang just said that during a solar eclipse, the moon can cover the sun. I was thinking, if it is a lunar eclipse, the earth will cover the light from the sun to the moon, right?"

Chai Che attacked Guo Jing.

"Ah, yes, yes!"

"That is to say, since Mr. Jiang and others said that Guo Shoujing of the Yuan Dynasty calculated the diameter of the earth, can they use some method to calculate the diameter of the moon during a lunar eclipse?"

Zhu Gaochi was startled when he heard this: "How to calculate it?"

"This" Chai Che said with a confused look on his face, "I haven't thought about it, I just have this idea."

After all, Chai Che didn't specialize in astronomy and mathematics, so it was just a flash of inspiration. He had such an idea, and it was not clear how to calculate the rest.

Hearing this, Zhu Gaochi did not embarrass him. After all, Zhu Gaochi did not expect to get answers from these two little officials. They were both ordinary scholars.

But Zhu Gaochi thought hard for a moment, but still didn't understand how the numbers of solar eclipses, lunar eclipses, the earth, and the moon, all these messy things, could be calculated.

There's no way, if you can't do something like mathematics, you really can't.

You can't figure it out just by thinking about it.

Therefore, Zhu Gaochi turned his hopeful eyes to the vicissitudes of the amplification wall.

——————

"The diameter of the earth is known, now we need to find the diameter of the moon, and then find the ratio of the diameter of the earth to the moon."

Jiang Xinghuo clarified the problem and then said: "The method is still the same as before."

"Pythagorean theorem?" Zhu Gaoxu asked.

"Definitely not." Zhuo Jing shook his head.

Jiang Xinghuo didn't intend to beat around the bush and said bluntly: "The proportional enlargement method just now."

"How can this be enlarged in proportion?" Zhu Gaoxu's clear eyes were full of stupidity.

"Eclipse."

Jiang Xinghuo pointed to the pattern on the ground and said: "We can calculate the time from when the moon first enters the shadow of the earth to when the moon is completely obscured, which is the first half of the lunar eclipse."

"Then we calculate the time from when the moon enters the Earth's shadow to when it leaves the Earth's shadow, which is the entire duration of the lunar eclipse."

"The ratio of these two times, which is the ratio of the diameter of the moon, to the shadow area of ​​the Earth that the moon passes through."

"And we only need to know the length of the shadow area on the earth and the diameter of the moon, and we can enlarge it in proportion!"

After hearing this, the three of them looked at the pattern on the ground, and for a moment they felt that it contained the most important principles of heaven and earth that could reach the stars and the moon.

Zhuo Jing raised his head and glanced at Jiang Xinghuo, sighing in his heart: "He really has the ability to reach heaven and earth. What Dao Yan said is actually true!"