Into Unscientific

Su Mansion.

In Lao Su's study.

This moment.

A thin but energetic little old man was sitting on a chair, staring at Wang Lin who was sitting opposite him with sharp eyes like a falcon.

It seems that in the next second, Zapelio's light will be released from the eyes, turning Wang Lin into scum:

"You are Wang Lin?"

Xu Yun rubbed the back of his neck, sighed and said:

"It's the villain."

Hearing this, the little old man immediately took out a letter from his body.

Snapped!

The little old man turned his wrist and slapped it heavily on the table:

"You wrote this letter?"

Xu Yun opened his mouth, wanting to say something like 'this letter was written by the master'.

But considering that he might be hanged and beaten for saying this, and his character design is not as funny as Wang Qiang, he had no choice but to say quietly:

"That's right."

"."

The little old man couldn't help but frowned, and said in a deep voice:

"Wang Lin, although I just met you for the first time, you don't look like that kind of treacherous person, and your counting skills are far superior to ordinary people, why do you like breaking chapters?

The old man knows a broken chapter dog. Keke, broken chapter party, his grave is probably ten feet high now. "

This kind of question Xu Yun has been asked countless times in his previous life, so he didn't have time to think about it, so he blurted out a sentence reflexively:

"There is no one else, but you are familiar with it."

Little old man:

"???"

Then he took a deep breath, suppressed the anger in his heart, and said seriously:

"Wang Lin, the old man has already arrived in Bianjing. Shouldn't the rest of the content be shown to the old man?"

Xu Yun seemed very cheerful this time, and took out a piece of paper from his body.

Spread out, spread out.

Press one of the corners, and push it to the old man, that is, in front of Jia Xian:

"Mr. Tongyu, here is the rest of the content, please read it."

Jia Xian's eyes lit up immediately.

I saw that he couldn't wait to take the paper, and began to read it seriously:

". The remaining one hundred and thirty-two thousand eight hundred and sixty-seven after undertaking, the calculation steps are as follows"

".The total of 340 feet into Lian by the method of 20 multiplications of the second Shang Dynasty, and 43,200 feet in square feet."

".Then take advantage of the lower method to enter Lian, a total of three hundred and sixty. The first method, the second method, and the lower three retreat, as before."

Jia Xian analyzed while watching, the whole process did not use any paper, pen or tools at all, it was all mental calculations!

". The third place in Shangshang counts three feet, and the total number of multiplication by the lower method is three hundred and sixty-three, and the total number of multiplication by the lower method is 44,289."

".Order Shangshang three feet to eliminate the reality, make the most of it, and get it"

"The number of one side of a cube."

Read the last sentence.

Jia Xian couldn't help closing his eyes, frowning slightly, as if he was checking the result.

After about a minute.

The little old man who seemed to have a hot temper slowly opened his eyes, exhaled a foul breath, and looked at Xu Yun with complicated eyes:

"The technical text is correct, and there is a third explanation for the method of seeking integrity in "Nine Chapters."

"Nine Chapters on Arithmetic".

This is an ancient book that all elementary school students in later generations have heard.

But many people have only heard its name, but they don't know why it is called "Nine Chapters of Arithmetic".

the reason is simple.

because it has nine chapters

That's right, it's that simple.

The nine chapters are Fang Tian, ​​Corn, Decline, Shao Guang, Shang Gong, Even Losing, Profit and Deficiency, Equation and Pythagorean.

Among them, in the chapter "Shaoguang", the most famous one should belong to the process of finding the cube root of 1860867. (Note: In the previous article, someone actually asked me who Shao Guangzhang was.)

Until 1100 A.D., the ancients only proposed two solutions for the cubic root.

The solution proposed by Xu Yun has never been discovered before.

The third solution!

same.

This is also a mystery that Jia Xian has been trying to solve in the first half of his life.

but unfortunately

Human energy is limited.

After discovering the mystery of the triangle, Jia Xian had no choice but to give up the problem of solving the cube root and put all his thoughts into the field of triangles.

This is like some Internet writers of later generations.

Originally, I was writing a book with an average order of one or two thousand, but the waistcoat suddenly published a hit, so I had no choice but to drop the former and write the latter.

Of course.

Xu Yun would definitely not do such a thing. Most of his books will only be written after they are sealed.

It's such a sad story.

Then Jia Xian took another deep breath, pointed to the corner of the envelope, and said to Xu Yun:

"Wang Lin, what do these symbols drawn by Xinjiao mean?"

Xu Yun poked his head for a few glances, and explained:

"You said these, these are Arabic numerals."

"Arabic numerals?"

Xu Yun nodded and continued:

"This is a character invented by the people of the Western Regions. It is relatively simple to write in contrast to the Chinese one, two, three, and four. Mr. Tongyu can also try to use it."

Arabic numerals are not like Yang Hui's triangle, they were indeed invented by the ancient Tianzhu people, and they do not belong to the buried ancient achievements of China.

Therefore, Xu Yun didn't deliberately take them as his own, after all, he didn't steal from the people of the country.

Right now, Huaxia Mathematics uses a small tool called chips.

It is a bit similar to the toothpicks of later generations, with a length of more than ten to twenty centimeters, so it is also called counting chips.

when calculating.

As long as these toothpicks are arranged in different patterns, calculations can be performed on behalf of each number.

In addition, sometimes if there is no toilet chip, it will be used

cough cough.

all in all.

Although this method is a little more convenient than written calculations, it is still a bit troublesome compared with Arabic numerals.

Although this thing was invented by the ancient third brother, it has to be admitted that it does have the convenience visible to the naked eye.

So after careful consideration.

Xu Yun finally decided to introduce the concept of Arabic numerals first.

After all, the amount of calculations needed in the future is destined to be large, and it is easier to have a convenient tool. Of course, high efficiency is better.

Of course.

Although Jia Xian does not know Arabic numerals and symbols, it does not mean that he does not understand these concepts:

Quite the opposite.

Whether it is addition, subtraction, multiplication and division or square cube extraction, mathematicians in ancient China have long studied this.

Therefore, it didn't take much time. Jia Xian and Lao Su at the side quickly understood and accepted the Arabic numerals.

At the same time, after understanding the content of the letter and the related mathematical concepts, Jia Xian's anger was calmed down, and he was not as irritable as before.

He coughed lightly, put away the letter and Xu Yun's paper calmly, and said to Xu Yun:

"Okay, Wang Lin, you don't hesitate to use such means to lure me, an old man, to Bianjing. Presumably it's not just for the simple introduction of Arabic numerals?"

In ancient China.

Although there is no later BBS or post bar in the mathematics circle, regional exchanges are relatively common under the organization of some relatively well-known and wealthy bigwigs.

Even in the Jiangnan area, the prototype of a small-scale newspaper similar to the Journal of Mathematics appeared.

This kind of newspaper is very cheap, you can order it for only a few pennies, and it is printed about once a month.

Considering the paper, shipping capacity, and printing costs during this period, this price is basically the same as losing money.

all in all.

If Xu Yun just wants to publish his own results, he only needs to contact a few 'editors' through Lao Su's relationship, and he can easily publish his solution.

So it's obvious.

Xu Yun took so much trouble to 'deceive' himself to Bianjing, he must have something to ask for.

Xu Yun didn't hold back on this, he was silent for a while, then cupped his hands at Jia Xian, and said:

"Mr. Tongyu is invited to come here this time. I do have an important matter that I hope you can help me with."

"What is it?"

"Study the lens formula."

Jia Xian was taken aback for a moment, and blinked blankly:

"Lens? Formula?"

The latter is understandable, but what the hell is the former?

Upon seeing this, Lao Su immediately took out a coarsely ground lens from his sleeve pocket and handed it to Jia Xian:

"This is it."

Jia Xian took the lens and looked it over, thoughtfully:

"It seems to be thick, but both sides are fuller, but judging by the material, it seems to be made of glass?"

Xu Yun nodded:

"good."

Jia Xian's eyes couldn't help becoming more puzzled:

"But what does it have to do with formulas?"

Xu Yun was silent for a moment, then said:

"Mr. Tongyu, the villain once heard you say a word, 'There are thousands of sundries in the world, and there is an inner reason for everything', right?"

Jia Xian nodded lightly, this sentence can be regarded as a motto in his life:

"good."

"Then, have you ever thought about the light that we see every day, and there is some kind of reason that is unknown?"

Jia Xian's pupils shrank immediately, and he subconsciously looked out the window:

"Light?"

Xu Yun thought for a while and took the pen and paper.

Draw a right-angled triangle with the right-angled side facing the right and the base pointing down.

Then he drew a few lines on each side, and marked 22 words such as "Sun Moon Mountains and Rivers, Holly Heart North" at one time.

Then I drew an inscribed circle, and said while writing:

"Mr. Tongyu, if you take them vertically and horizontally from the center and outside of the circle, you can get fifteen shapes, big and small, all without strange zeros."

"The three vertices are the sky, the earth, and the stem. The center of the inscribed circle of the triangle of the sky and the earth is called the heart."

"The vertical line passing through the center intersects with the triangle and the inscribed circle at the sun, south, and north points from top to bottom."

"The horizontal line crossing the center intersects with the triangle and the inscribed circle at the river, east, and west points from left to right."

"The vertical line passing through the east and the horizontal line passing through the south are both tangent lines of the inscribed circle. They intersect the heaven-earth stem triangle at the four points Gen, Kun, Shan, and Moon respectively, and intersect at the Xun point."

"The combination of the four elements of Qian Kun Xun Gen can form a square."

"The vertical line crossing the moon meets the east-west horizontal line at Qingdian, and the dry side of the ground meets the spring point. The horizontal line passing the mountain meets the north-south vertical line at Zhudot, and the heavenly stem side meets Jindian. These two lines intersect at Pandian .”

"The last horizontal line passing the sun meets the sky stem at the Dan point, and the vertical line crossing the river meets the ground stem at the Xi point."

"The above points total 22."

When Xu Yun first started drawing, Jia Xian's gaze was somewhat casual.

I don't know why Xu Yun talked about the triangle when he was talking about light.

But watch and watch.

His expression gradually became more dignified.

Wait until the end.

His look is nothing but

Horrified!

As an expert on triangle problems, Jia Xian put forward an idea a long time ago. Or a theory:

"Pythagorean strings are merged to form harmony, subtracted to compare, equal to change, multiplied to segment, self-multiplied to product and power."

This is the famous thirteen pictures of Pythagorean shares:

Refers to hook (a), strand (b), string (c), Pythagorean (b-a), hook (c-a), strand (c-b), Pythagorean and (a+b), hook and ( a+c), chord sum (b+c), chord sum (c+(b-a)), chord sum (c+(a+b)), chord sum ((a+b)-c), chord Compare (c-(b-a)).

It can be said like this.

Jia Xian has completed all the relationships between the Pythagorean string and its sum and difference, and has put aside the calculation problem itself of "Nine Chapters" and conducted an abstract analysis of the Pythagorean problem.

The picture drawn by Xu Yun is not only very similar to him in concept, but even more vivid and concise than the concept he put forward!

Looking at the horrified Jia Xian, Xu Yun couldn't help but let out a sigh of relief:

It seems that I have succeeded in 'asking God'.

See here.

Presumably many students have already understood the origin of Xu Yun's drawings:

That's right.

It is "Che Yuan Hai Jing"!

"Measuring the Circle Sea Mirror".

This is a masterpiece of mathematics written by Li Ye, a mathematician in the Jin and Yuan Dynasties, which is also the famous Tianyuan technique.

Early 1234 AD.

In Tongchuan, Li Ye obtained a calculation book written by Dongyuan, which contains the theory of nine guests.

Therefore, Li Ye combined many achievements of Dong Yuan and Jia Xian to summarize Pythagorean Rong Yuan into a complete system.

And more importantly.

After "Measuring Yuan Hai Jing", Li Ye raised half of Huang Fangmi's question based on Pythagorean Rong Yuan.

Yes.

Half of Huang Fangmi.

That is, the paraxial approximation of the approximate quantitative description of Kirchhoff's diffraction formula.

Prototype!

After drawing the dividing line.

Xu Yun took Lao Su's lens and placed it upright on the center of the inscribed circle he drew.

Then pointing to the line with the character 'green' in it, he said to Jia Xian:

"Look."

Only at this moment.

Affected by the refraction effect of the lens, the 'green' line inside and outside the mirror suddenly had a deflection visible to the naked eye!

Then Xu Yun wrote 'sky' on the outside of the blue line, removed the lens, and wrote 'earth' on the deflected blue line inside.

Then he wrote:

Let the position of the lower end of the blue line be Xuan, and the deflection end be yellow.

The positions of the distance circle are flood and barren respectively.

Then there is:

Heaven = Earth.

Heart North = Xuan + (Hong - Huang) + (Hong - Mountain Heart).

at the same time:

(δ/2xuan) Hong + Huang is far smaller than pi.

(Hong+Hong)×δ=Xinbei×? ? (Desolation + Xin Zhu) ×? =Hong-Shanxin×? .

After writing these, Xu Yun said to Jia Xian:

"Mr. Tongyu, this is some kind of deflected solution passed down by the villain's ancestors, but there are several unknown symbols and derivation ideas in it.

At the same time, this kind of solution is the necessary data to prepare a certain object, so I can only invite Mr. to come, hoping to help the villain. "

Jia Xian was silent for a moment, then looked at the lens on the table again, and said:

"Wang Lin, the third solution to the "Shaoguang" chapter is the old man's long-cherished wish. Originally, the old man thought that there would be no hope of someone to solve it before he died, but today you gave me a big surprise.

The ancients said.

If you hear the Tao in the morning, you can die in the evening.

The feeling of resolving doubts is very heavy, the old man must never forget that calling you a broken dog earlier was just a moment of anger.

Now even if it is to repay your affection, the old man will never shirk the matter of the lens formula.

But Wang Lin.

The old man has never dabbled in the lens, so it is difficult to guarantee that he will get something. He can only do his best and obey the destiny.

If you can't solve this problem, the old man will divide half of the family wealth with you as a reward. "

Xu Yun was taken aback when he heard the words, and a cold sweat suddenly broke out on his forehead.

Damn.

This big guy is actually too upright, isn't he, cooperating with the ancients and giving them a pension directly?

So he hastened to say:

"Mr. Tongyu is serious. If you are willing to help, the villain is already grateful. Please don't talk about raising funds."

Jia Xian glanced at him, did not speak, but turned around and cupped his hands at Old Su:

"Brother Zirong, can I borrow some paper and pen?"

Old Su smiled and saluted his old friend:

"Mr. Tongyu, but it doesn't hurt to use it."

Jia Xian nodded when he heard the words, walked to the table, and was about to start the calculation.

But at this moment.

Suddenly, Old Du Guan's voice sounded from outside the house:

"Master, Mr. Yang Huai, Mr. Jin Qu and others have already left the courtyard."

Note:

In the afternoon, I chatted with an old pigeon, who was about to open a new book, but found that I hadn’t logged in for a long time, and I forgot the password of the author’s account, hahahaha

In addition, I am exhausted from writing this chapter, purely original derivation