Su Mansion.
In Lao Su's study.
At this moment.
A thin but energetic little old man was sitting upright on a chair, staring at Wang Lin sitting opposite him with sharp eyes like a hawk.
It seemed that in the next second, Zaipei Liao's light would be emitted from his eyes, turning Wang Lin into a scumbag:
"Are you Wang Lin?"
Xu Yun rubbed the back of his neck and sighed:
"Exactly the villain."
When the little old man heard this, he immediately took out a letter from his body.
Snapped!
I saw the little old man flipping his wrist and slamming it on the table:
"Did you write this letter?"
Xu Yun opened his mouth, wanting to say something like "This letter was written by the master".
But considering that I might be hung up and beaten if I said this, and my personality was not that funny like Wang Qiang’s, I had no choice but to say quietly:
"That's right..."
"..."
The little old man couldn't help but frown and said in a deep voice:
"Wang Lin, although I have just met you for the first time, I don't think you look like such a treacherous person, and your calculation skills are much higher than ordinary people. Why do you like to break chapters?
I know a dog in pieces... Ahem, a dog in pieces. Now his grave is probably about one foot high. "
Xu Yun had been asked this question countless times in his previous life, so he blurted out a sentence like a conditioned reflex without even having time to think:
"Nothing but familiarity with your hands."
Little old man:
"???"
Then he took a deep breath, suppressed the anger in his heart, and said seriously:
"Wang Lin, now that I have arrived in Bianjing in person, should I show you the remaining content?"
Xu Yun seemed very happy this time and took out a piece of paper from his body.
spread out, spread out.
Pressing one corner, he pushed it in front of the old man...that is, Jia Xian:
"Mr. Tongyu, the rest of the content is here. Please take a look."
Jia Xian's eyes suddenly lit up.
I saw him eagerly taking the paper and starting to read it seriously:
"....The remaining one hundred and thirty-two thousand eight hundred and sixty-seven have been taken over. The calculation steps are as follows..."
“…..The next step is to take twenty times to descend the Dharma into Lian, a total of three hundred and forty, and by Lian to enter the square, a total of 43,200 feet.”
"...and then take advantage of the lower method to enter the Lian, a total of three hundred and sixty...the first side, the second Lian, and the third 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 person in Shang Shang can count three feet. The total number of three hundred and sixty-three is to enter Lian by Dharma, and the total is forty-four thousand two hundred and eighty-nine by Lian....."
“….. The fate is up to three feet to eliminate the reality. When the fitness is exhausted, you will get…”
"The number of sides of a cube."
Read the last sentence.
Jia Xian couldn't help but close his eyes, frowning slightly, as if he was checking the results.
About a minute passed.
The little old man who seemed to have a hot temper slowly opened his eyes, exhaled a breath of turbidity, and looked at Xu Yun with complex eyes:
"The writing is correct, and there is a third explanation for the law of seeking integrity in "Nine Chapters"."
"Nine Chapters of Arithmetic".
This is an ancient book that all primary school students of later generations have heard of.
But many people have only heard of its name, but don't know why it is called "Nine Chapters of Arithmetic".
the reason is simple.
Because it has nine chapters in total...
Yes, it's that simple...
The nine chapters are Fangtian, Millet, Shaofen, Shaoguang, Shang Gong, Loss of Balance, Insufficiency of Profit, Equation and Pythagorean.
Among them, in the chapter "Shao Guang", the most famous one should be the process of developing the cube root of 1860867. (Note: In the previous article, someone actually asked me who Shao Guangzhang was...)
As of 1100 AD, the ancients had only proposed two solutions to open square roots.
The solution proposed by Xu Yun is something that has never been discovered before...
The third solution!
same.
This is also a mystery that Jia Xian has always wanted to solve in the first half of his life.
But it's a pity...
Human energy is limited.
After discovering the mystery of triangles, Jia Xian had no choice but to give up the problem of solving cube roots and devoted all his attention to the field of triangles.
This is like some Internet writers in later generations.
Originally, I was writing a book that had both one and two thousand orders, but suddenly a hit book came out of the vest, so I had no choice but to write the former and write the latter.
Of course.
Xu Yun would definitely not do such a thing. Most of his books were blocked before he wrote the next one.
.....This is such a sad story.
Then Jia Xian took a deep breath again, pointed to the corner of the envelope, and said to Xu Yun:
"Wang Lin, I wonder what the symbols drawn by Xinjiao mean?"
Xu Yun looked over his head and took a few glances, then explained:
"You said these, these are Arabic numerals."
"Arabic numerals?"
Xu Yun nodded and continued:
"This is a character invented by people from the Western Regions. It corresponds to the Chinese characters one, two, three and four. It is relatively simple to write. Mr. Tongyu can try to use it."
Arabic numerals are not like Yang Hui's triangle. They were indeed invented by the ancient Tianzhu people and are not among the buried achievements of ancient China.
Therefore, Xu Yun did not deliberately take them as his own. After all, he was not stealing from the country.
At present, what is used more frequently in Chinese arithmetic is a small tool called chips.
It is somewhat similar to the toothpicks of later generations, with a length of more than ten to twenty centimeters, so it is also called a calculation tool.
when calculating.
As long as these toothpicks are arranged in different styles, they can represent various numbers for calculations.
In addition, sometimes if there is no toilet seat, I will use it...
Ahem.
all in all.
Although this method is more convenient than pen calculation, it is still a bit troublesome compared with Arabic numerals.
Although this thing was invented by the third brother in ancient times, I have to admit that it does have 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 required in the future is destined to be large. It is easier to have a convenient tool. Of course, it is better to be more efficient.
Of course.
Although Jia Xian does not recognize Arabic numerals and symbols, this does not mean that he does not understand these concepts:
Quite the opposite.
Whether it is addition, subtraction, multiplication and division or square root and cube root, ancient Chinese mathematicians have long studied this.
Therefore, it took little time for Jia Xian and Lao Su beside him to quickly understand and accept Arabic numerals.
At the same time, after understanding the content of the letter and related mathematical concepts, Jia Xian finally calmed down and became less irritable than before.
He coughed slightly, put away the letter and Xu Yun's paper calmly, and said to Xu Yun:
"Okay, Wang Lin, you did not hesitate to use such means to lure an old man like me to Bianjing. It must be more than just to introduce Arabic numerals, right?"
In ancient China.
Although there is no later BBS or post bar in the mathematics circle, regional exchanges are still relatively common under the organization of some relatively well-established and wealthy bosses.
Even in the Jiangnan area, prototypes of small-scale newspapers and periodicals similar to Mathematics Journal appeared.
This kind of newspaper is very cheap. You can order it for only a few cents and print it about once a month.
Taking into account the paper, transportation capacity, and printing costs during this period, this price is basically the same as losing money.
all in all.
If Xu Yunruo just wanted to publish his results, he only needed to contact a few 'editors' through Lao Su's relationship, and he could easily make his solution public.
So it's obvious.
Xu Yun went to such great lengths to 'cheat' himself to Bianjing, so he must have something to ask for.
Xu Yun didn't care about this either. He was silent for a moment, then he cupped his hands towards Jia Xian and said:
"I invite Mr. Tongyu to come here this time. I really have an important matter that I hope you can help me with."
"What's the matter?"
"Study the lens formula."
Jia Xian was stunned for a moment and blinked blankly:
"Lens? Formula?"
The latter is understandable, but what the hell is the former?
When Lao Su on the side saw this, he immediately took out a rough-polished lens from his sleeve pocket and handed it to Jia Xian:
"This is it."
Jia Xian took the lens and looked at it, and said thoughtfully:
"It seems to be sweet, but the sides are fuller, but judging from the material...it seems to be made of glass?"
Xu Yun nodded:
"good."
Jia Xian's eyes couldn't help but become more and more confused:
"But what does it have to do with the formula?"
Xu Yun was silent for a moment and said:
"Mr. Tongyu, I once heard you say, 'There are all kinds of things in the world, and everything has its own truth,' right?"
Jia Xian nodded slightly. This sentence can be regarded as a motto in his life:
"good."
"Then sir, have you ever thought that...the light we see every day has some unknown reason?"
Jia Xian's pupils suddenly shrank and he subconsciously looked out the window:
"Light?"
Xu Yun thought for a while and took out the pen and paper.
Draw a right triangle with the right side facing right and the base down.
Then he drew a few lines on each edge and marked 22 words at once, including "Sun, Moon, Mountains and Rivers, Holly Heart North".
Then he drew another inscribed circle and said while writing:
"Mr. Tongyu, if you take it vertically and horizontally from the center of the circle and outside the circle, you can get fifteen shapes, big and small, with no oddities."
"The three vertices are heaven, earth, and stems. The center of the inscribed circle of the triangle of heaven, earth, and stems is called the center."
"The vertical line passing through the center intersects the triangle and the inscribed circle at the three points of sun, south and north from top to bottom."
"The horizontal line passing through the center intersects the triangle and the inscribed circle at three points: Sichuan, east and west from left to right."
"The vertical line passing through the east and the horizontal line passing through the south are both tangents of the inscribed circle. They intersect the heaven and earth triangle at the four points of Gen, Kun, Shan and Yue respectively, and intersect at the Sunda point."
"The combination of Qiankun, Xungen and Gen can form a square."
"The vertical line crossing the moon intersects the east-west horizontal line at the green point, and intersects the ground stem edge at the spring point. The horizontal line crossing the mountain intersects the north-south vertical line at the vermilion point, and intersects the sky stem edge at the golden point. And these two lines intersect at the pan point .”
"The last horizontal line passing through the sun meets the sky stem at the day point, and the vertical line crossing the river intersects the earth stem edge at the eve point."
"The above points are recorded as 22 in total."
When Xu Yun first started drawing, Jia Xian's eyes were still a bit casual.
I don’t know why Xu Yun talks about light, but why he talks about triangles again.
But look at it.
His expression gradually became more solemn.
Wait until the end.
All he looked like was...
Shocked!
As an expert on triangle issues, Jia Xian put forward an idea...or theory:
“Pythagorean strings combine to form sum, subtraction to form comparison, equality to form change, multiplication to form a segment, self-multiplication to form product, and power to form.”
This is the famous Pythagorean Thirteen Picture:
Refers to hook (a), stock (b), string (c), Pythagorean ratio (ba), hook string ratio (ca), stock string ratio (cb), Pythagorean sum (a+b), hook string sum ( a+c), strands and strings (b+c), strings and strings (c+(ba)), strings and strings (c+(a+b)), strings and strings ((a+b)-c), strings and strings Compare (c-(ba)).
It can be said like this.
Jia Xian has completed all the relationships between Pythagorean strings and their sums and differences. He has put aside the "Nine Chapters" calculation itself and conducted an abstract analysis of the Pythagorean problem.
The picture drawn by Xu Yun is not only very similar to him in concept, it is even more vivid and concise than the concept he proposed!
Looking at the horrified Jia Xian, Xu Yun couldn't help but let out a breath:
It seems that my 'invitation to God' was successful.
See here.
Many students must have understood the origin of the pictures drawn by Xu Yun:
That's right.
It's the "Seascope for Measuring the Circle"!
"Measuring the Circle of the Sea".
This is a masterpiece of mathematics written by Li Ye, a mathematician in the Jin and Yuan Dynasties, which is also the famous Tianyuan Shu.
Early 1234 AD.
Li Ye obtained an arithmetic book from Dongyuan in Tongchuan, which contained the theory of Nine Guests.
So Li Ye combined the many achievements of Dongyuan and Jia Xian to summarize Pythagorean Rongyuan into a complete system.
And more importantly.
After "Measuring the Circle in the Sea", Li Ye raised the question of half a Huang square power based on the Pythagorean circle.
Yes.
Half a piece of yellow square power.
That is, the paraxial approximation of Kirchhoff's diffraction formula approximately quantitatively describes...
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 he pointed to the "green" line and said to Jia Xian:
"Look."
I only see this moment.
Affected by the refraction effect of the lens, the 'green' line inside and outside the mirror suddenly showed a deflection visible to the naked eye!
Xu Yun then wrote "天" on the outside of the green line, moved the lens, and wrote "地" on the inside of the green line that had been deflected.
Then he wrote:
Let the lower end of the green line be Xuan and the deflected end be yellow.
The positions away from the circle are flood and wilderness respectively.
Then there is:
Day=¿ land.
Heart North²=Xuan²+(Hong-Huang)²+(Hong-Shanxin)².
at the same time:
(δ/2Xuan) Hong²+黄² is much smaller than pi.
(Hong+Hong)×δ=心北×? ? (Huang+Xinzhu)×? =Hong-Shanxin×? .
After writing this, Xu Yun said to Jia Xian:
"Mr. Tongyu, this is some kind of twisted solution passed down by the villain's ancestors, but there are several unknown symbols and derivation methods that are unknown.
At the same time, this kind of solution is necessary data for preparing a certain object, so I can only ask Mr. to come, hoping to help the villain. "
Jia Xian was silent for a moment, looked at the lens on the table again, and said:
"Wang Lin, the third solution to the chapter "Shao Guang" is my long-cherished wish. Originally, I thought that no one would be able to solve it until I die, but today you gave me a big surprise.
The ancients said.
If you hear the Tao in the morning, you will die in the evening.
The feeling of clearing up confusion is very important, I must not forget that calling you a broken dog before was just a momentary remark.
Now, even if it is to repay your kindness, I will never shirk the matter of the lens formula.
But Wang Lin.
I have never dabbled in the subject of lenses, so there is no guarantee that I will get something. I can only do my best and obey fate.
If you can't solve this problem, I will divide half of my family wealth with you as a reward. "
Xu Yun was stunned when he heard this, and a cold sweat broke out on his forehead.
Oh my god.
Isn't this big boss too upright? Like the people in ancient times gave away pensions directly if they didn't agree with each other?
So he quickly said:
"Mr. Tongyu's words are serious. I would like to thank you for your help. Please don't talk about raising funds any more."
Jia Xian glanced at him and said nothing. Instead, he turned around and cupped his hands towards Lao Su:
"Brother Zirong, can you borrow some paper and pen?"
Lao Su smiled and saluted his old friend:
"Mr. Tongyu, it doesn't matter if you use it."
Jia Xian nodded after hearing this, walked to the table, picked up a pen and paper and started calculating.
.......
Note:
I was chatting with an old pigeon in the afternoon. He was going to open a new book, but he found that he hadn’t logged in for a long time and forgot the password for his author account. Hahahaha
Also, I was exhausted from writing this chapter, it is purely original derivation...
