The emotional atmosphere has come to this point, and if the sun is not measured, the discussion group of several people will obviously not stop.

Zheng He held his long hair with great interest and asked.

"So, how do we calculate the distance between us and the sun?"

Jiang Xinghuo didn't answer this question directly, he glanced at the other party's neck exposed because of 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 get used to Zhu Di, the rebel and murderer, he didn't seem to have any special opinions on Zhu Gaoxu.

Approximately is felt. To each his own master?

Or do you disdain to worry about juniors?

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

"The Sutra of Zhou Ji" once recorded a conversation between Shang Gao and Zhou Gong, Shang Gao said: ...... Therefore, the folding moment, the hook wide three, the stock repair four, the meridian five. This is where the Pythagorean theorem comes from. ”

That is to say, when the two right-angled sides of a right-angled triangle are 3 (hook) and 4 (strand) respectively, the radius corner (string) is 5, and later generations simply said this theorem as "Pythagorean four strings five", according to which the Pythagorean theorem is also called the quotient high theorem.

Zhao Shuang of the Three Kingdoms period made a detailed annotation of the Pythagorean theorem in the "Zhou Ji Sutra", which was recorded in the "Nine Chapters of Arithmetic" "Pythagorean multiplication, and divide by the square, that is, the string", Zhao Shuang created a "Pythagorean square diagram", using the combination of numbers to obtain the method, giving a detailed proof of the Pythagorean theorem.

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

Jiang Xinghuo said lightly.

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

"Hiss~"

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

After all, the predecessors have already told you how to operate, you just need to follow it, and it is not for you to invent the twist scale experiment, the tower throwing ball experiment, and you don't need to understand "why Pan Jinlian's bamboo pole fell on Ximenqing's head instead of flying into Chang'e's hands".

But for the people of Daming.

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

"What does the Pythagorean theorem have to do with measuring our distance from the sun?"

As Jiang Xinghuo's founding disciple, Zhu Gaoxu knew his inherent impression in Mr. Jiang's heart, so he gave full play to his excellent style of learning to ask questions if he didn't understand.

"It matters."

Jiang Xinghuo continued to draw.

It can't be helped, geometry is really useful sometimes.

The moon ———— the sun

丨

earth

Jiang Xinghuo said: "Let me first tell you an important precondition, that is, the moon itself does not shine, and the light of the moon is reflected from the sun. ”

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

The silver coin of the Eight Si Pa Wen that Li Jinglong left to him.

"The Moon."

The old and the young looked at each other.

"Oh"

Referring to the deer as a horse belongs to yes.

However, seeing that the silver coin was aimed at the sun and began to reflect, the three of them also understood what Jiang Xinghuo meant.

"Then I ask you, when will the moon, the sun, and the earth form a right angle with the moon as a point and the sun and the earth at the same time?"

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

And looking at Jiang Xinghuo's movements, the old man Zhuo, who was twisting his beard, reluctantly pinched off a beard again. Because I was so excited.

"At the time of the String Moon!"

"That's right."

The so-called quarter moon is divided into the first quarter moon and the second quarter moon, which is due to the continuous change of the position of the sun, earth and moon, and the moon phase has a change in profit and loss, which the ancients were also fully aware of, so including the calculation of solar eclipses, lunar eclipses or something, the Ming Dynasty followed the Yuan Dynasty's "Time Calendar", and it was also possible to calculate seven or eight times ten times.

Oh yes, and there's one more point that the average person can easily overlook.

Why is a month called a "month"?

This is because the moon's surface from the new moon to the full moon towards the earth is gradually illuminated by the sun and gradually increases, and the moon phase changes from loss to profit, and the moon phase change period is 29.53 days, which is about 30 days.

30 days is a "month".

The so-called upper and lower quarter moons, judging from the phases of the moon, can still see the complete edge of the moon arc as a bowarm, in making a dotted line to connect the two ends of the arc, imagine as a bowstring, the string on the upper side of the moon is the first quarter of the moon, and the lower side is the lower quarter of the moon.

That is, a ○ is cut in half diagonally from northeast to southwest or vice versa, which is the appearance of the upper and lower quarters.

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

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

It was precisely because he understood this truth that Old Man Zhuo excitedly pinched off a precious beard that had little left.

Old man Zhuo pointed to the earth, moon, and sun painted on the ground with great interest.

"As long as it is a quarter moon, according to the hours and moments calculated by the Qin Tian in the past dynasties, you can get a right angle, and 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 angle only needs to be reduced to come out!"

The more Old Man Zhuo spoke, the more excited he became, and even danced with his hands.

"And the angles of the three corners of the triangle are calculated, assuming that the distance between the earth and the moon is one unit, then the distance between the earth and the sun, the distance between the moon and the day can also be calculated, and then, then."

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

The Pythagorean theorem can only be derived from three sides and three corners, and there is no way back!

"And then what?"

Jiang Xinghuo reminded: "According to the diameter of the earth, the diameter of the moon is calculated, and then the diameter of the sun is derived. ”

"How?"

Jiang Xinghuo began to draw on the ground again, and he said while drawing: "The Pythagorean theorem calculates the proportion of the distance between the earth, the moon, and the sun (assuming that the distance between the earth and the moon is 1 unit) and angle, so you can use the same scale to calculate the diameter of the sun." ”

Earth—Moon—Sun

After painting, Jiang Xinghuo explained the principle.

"Because when the three are in a line, that is, when the sun is eclipse, the moon can almost perfectly block the sun."

"Then from the earth, the size of the sun and the moon is basically the same, which means that the perspective of looking at the moon from the earth and looking at the sun is the same, so since the Pythagorean theorem knows that the distance from the sun to the earth is about several times the distance from the moon to the earth, then it can be inferred in equal proportions that the diameter of the sun is several times the diameter of the moon, and it can be calculated with a very basic proportional relationship of similar triangles."

Seeing that the eldest disciple seemed to understand a little, Jiang Xinghuo directly drew two triangles next to each other, and then enlarged the second one in equal proportions, and Zhu Gaoxu understood.

"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 and the moon, and get the diameter of the moon, and then we can reverse the diameter of the sun?"

Old man Zhuo reacted.

"Exactly."

Jiang Xinghuo nodded approvingly, and then said, "Then think about it, how to calculate the ratio of the diameter of the earth and the moon?" ”

——————

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

In the secret room, Zhu Gaochi began to engage in "three stinky generals to top Zhuge Liang", and he looked at Guo Jin and the firewood cart.

Not to mention, brainstorming is much better than meditating alone.

"Your Highness, the minister has an idea." The firewood cart said suddenly.

"Tell me about it."

Zhu Gaochi said busily.

"Mr. Jiang just said that when a solar eclipse, the moon can cover the sun. Xiao Chen was thinking, if it is a lunar eclipse, that is, the earth obscures the light of the sun to the moon, right? ”

The firewood car scolded Guo Jin.

"Ah, yes, yes, yes!"

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

Zhu Gaochi was stunned when he heard this: "How do you calculate it?" ”

"This" Chai Che looked embarrassed, "Xiao Chen didn't think about it, but he just had such an idea." ”

After all, the diesel car is not specialized in astronomy and mathematics, so it is just a flash of inspiration, and there is such an idea, and it is not very clear how to calculate the rest.

Hearing this, Zhu Gaochi didn't embarrass him, after all, Zhu Gaochi didn't expect to get an answer from these two little officials, they were ordinary readers.

But Zhu Gaochi pondered for a while, but he still didn't understand how the number of solar eclipses, lunar eclipses, earth, and moon could be calculated in a mess.

No way, there is such a thing as mathematics, it won't be, it really won't.

You can't think of it just by thinking about it.

Therefore, Zhu Gaochi looked at the wall of amplification that had been full of vicissitudes.

——————

"Now that the diameter of the Earth is known, the diameter of the Moon is now required, and then the ratio of the diameter of the Earth and the Moon is obtained."

Jiang Xinghuo clarified the problem, and then said: "The way, it's still the old way just now." ”

"The Pythagorean theorem?" Zhu Gaoxu asked.

"Definitely not." Zhuo Jing shook his head.

Jiang Xinghuo didn't plan to go around in circles, and said bluntly: "The equal scale magnification method just now." ”

"How can this be scaled up?" Zhu Gaoxu's clear eyes were full of stupidity.

"Lunar eclipse."

Jiang Xinghuo pointed to the pattern on the ground and said: "You can calculate the time when the moon just begins to enter the earth's shadow and the moon is completely obscured, that is, the first half of the lunar eclipse. ”

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

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

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

Hearing this, the three of them looked at the pattern on the ground again, and in an instant, they felt as if it contained the truth of heaven and earth that could pick the stars and take the moon.

Zhuo Jing glanced up at Jiang Xinghuo, and sighed secretly in his heart: "If you really have the ability to penetrate the heavens and the earth, what Dao Yan said is true!" ”

(End of chapter)