Wang Ou found it interesting and asked, "Can this set of symbols be taught to slaves?
"Of course." Li Mu squatted down, picked up a branch from the ground, and wrote down nine numbers from 1 to 9, then left a space behind 9 and wrote 0. Wang Ou also squatted next to him,
Watch carefully.
"Starting from 1, all the way to 9, corresponding to one to nine, the following 0 is zero. If you want to record a number larger than nine, add one digit in front." Li Mu wrote a '10' in the following line and explained: "
The 0 position represents one. The digit added in front represents ten. Now one here is o, which means none. The previous one here is 1, which represents a ten, which is 10."
Li Mu himself felt that he didn't explain it clearly, but Wang Ou actually understood it. He also took a branch and wrote 15 on the ground, saying: "Does this mean fifteen? One ten, five one."
"Yes, yes!" Li Mu nodded vigorously and thought to himself, she is indeed a daughter of a famous family, and she is indeed very smart. Li Mu took out the Arabic numerals and planned to use them. Since Wang Ou was curious and so smart, he let her be his
The first student of course couldn't be more suitable.
Li Mu wrote five more symbols '+''-''x''÷''=' on the ground and said: "When I was in Dingxiang, I read the "Zhou Bi Suan Jing" brought by my sworn brother Li Siwen.
After reading it, I felt it was complicated. The calculation techniques recorded in it required several lines of writing to calculate a simple problem, which was really troublesome for me."
"This matter has always been in my mind. I thought I would be able to find a solution after arriving in Chang'an. When I lived in my adoptive father's house, I asked several old accountants and they all used the calculation method.
, Later I worked in the Ministry of Industry and found that the craftsmen who worked did not even know how to use algorithms. They relied on the experience passed down from their ancestors to deal with the problem. They couldn't explain how they calculated it. "
Li Mu sighed: "I thought about it, and it was not an option to continue like this. So I invented this set of symbols for counting." Li Mu pointed to the ground and said, "After counting was feasible, I experimented again and again.
After inventing these five symbols countless times, I finally completed a set of my own algorithms. I call it the Four Arithmetic Algorithms."
"Four arithmetic operations? Algorithms you invented yourself?" Wang Ou's tone was full of incredulity. She had studied arithmetic, and had learned more than one arithmetic classic. The Wang family in Taiyuan had a rich collection of books, and Wang Ou had been reading since she was a child.
She has studied "Zhou Bi Suan Jing", "Nine Chapters of Arithmetic", and "Island Arithmetic Sutra". Her arithmetic level is such that even if she takes part in the 'Ming Suan' section of the imperial examination, she can easily come out on top. Therefore, she is well aware of the profoundness of arithmetic.
.
All the existing arithmetic scriptures were derived by sages who spent their entire lives summarizing the experience of their predecessors. And how old was Li Mu that he actually boasted that he had invented an algorithm in Haikou?
Wang Ou didn't believe it.
Li Mu heard it and felt a little unhappy. If anything else, he didn't dare to boast. When it came to mathematics and numbers, he still dared to say that he was proficient. In his previous life, he did data balancing and dealt with numbers every day. Sometimes in order to correct a skill
He has to get up in the middle of the night and work overtime to figure out formulas. He is very sensitive to numbers.
Even if his job is put aside, he is still a college graduate. He has passed calculus, can he still do the four arithmetic operations?
Li Mu smoothed the writing on the ground with his hand and said, "These five symbols represent the five meanings of addition, subtraction, multiplication, and division."
"Addition and subtraction are very simple. It has been recorded in Zhou Bi Sutra, but for multiplication and division, I discovered a simple calculation method."
"There is a 'Jiu Yin Song' in the Zhou Bi Suan Sutra, which records simple multiplication formulas. For example, two two equals four, nine nine eighty one, etc. However, it can only perform a few operations. If it is a larger number, it will
I can’t calculate it anymore. But with my symbol and my algorithm, I can calculate numbers of any size.”
Li Mu wrote 23x18 on the ground and explained to Wang Ou: "For example, this is twenty-three times eighteen. The numbers at both ends of the symbol are named factors according to the Jiu Yin song. We can use the second factor
Units digit 8, first multiply the units digit 3 of the first factor to get 24, we write it down, and then use 8 to multiply the tens digit 2 of the first factor to get 16, because this 2 is in
The tens digit, so we write 16 in front, so we get a hundreds digit, two tens digits, and a ones digit. We add the two numbers in the tens digit to get 8, so we get 184."
Li Mu wrote 184, and then continued writing below: "Then we use the tens digit 1 of the second factor and multiply it again according to the method just now. Because this 1 is the tens digit, we get 23 tens, using 23
Add 18, and you get 41, and add your 4, and you get 414. How about it, is it very simple?"
Don't look at Li Mu's cumbersome words, but for the mathematics level of the Tang Dynasty, this was already very fast. So much so that Wang Ou couldn't believe whether the numbers Li Mu calculated were correct. He kept these two numbers in his heart.
, I plan to use the method I have learned to calculate again when I get home to verify whether Li Mu’s algorithm is correct.
"Let's talk about division again. Division can be regarded as the inverse calculation of multiplication. We just got 23x18=414, then we divide 414 by 18. Starting from the high digit of the dividend, we will first look at the first digit of the dividend.
, if it is not enough to divide, you have to look at one more digit. The resulting number is called the 'quotient', and the remaining number is called the 'remainder'. Whichever digit you divide to, you must write the quotient on that digit.
, the remainder of each division must be smaller than the divisor. After finding the highest digit of the quotient, if any digit of the dividend is not enough to quotient 1, write 0 on that digit..."
Li Mu has tried hard to speak in a simple and easy-to-understand manner, but he has long forgotten how the old dean taught him when he was learning addition, subtraction, multiplication and division. Now he has long developed the instinct of mental arithmetic, and these steps are in his calculations.
Sometimes, it is almost ignored. There is really no way to put it more simply.
Li Mu talked a lot, and Li Mu was a little confused. He glanced at Wang Ou, who was squatting next to him and frowning in deep thought. He was very unsure whether she could understand.
Wang Ou didn't speak for a long time. Suddenly he picked up a branch and wrote 12x13 on the ground. Then he calculated step by step according to Li Mujiao's multiplication method and got 156. Then he divided 156 by 12 according to Li Mujiao's division method and got 13.
." Li Mu clapped his hands in excitement, grabbed Wang Ou's arm, and said excitedly: "You are so smart! You can understand what I said so randomly! It's really amazing!"
When Wang Ou was grabbed by Li Mu's arm, she subconsciously wanted to shrink back, but when she saw Li Mu's excited look, a trace of hesitation flashed in her eyes and she did not do so. This was the first time that a man took the initiative to grab her arm, and she felt something surge in her heart.
It was a very strange feeling, but she was no longer an ignorant girl. She was no longer overly shy, and her cheeks were just slightly red.
She multiplied 12 by 13 because she had just delivered twelve carts of cloth yesterday, with thirteen pieces of cloth on each cart. The result of 156 was actually found by counting the pieces one by one.
This accurate answer can be verified by verifying Li Mu's algorithm, and we can naturally know whether it is accurate or not.
The result surprised her. Li Mu's algorithm was so accurate and accurate. The seventeen-year-old man in front of her actually invented an algorithm by himself. And it was so simple that he hardly needed to know any arithmetic to use it.
How did he do it? He is so capable!
If someone really has such a genius, wouldn’t it become a joke for those who study sutra calculation in this world to know how to master the sutra?
Wang Ou is not a person who gets angry easily, but at this moment she can't help but want to find an explanation for the arithmetic she has learned for so many years when she was young. She thought about it and suddenly remembered a book she had read in the Northern Wei Dynasty, "Qiu Jian Suan".
There is an unsolvable question in the Classic of Chinese Medicine, this title is "The Question of One Hundred Chickens". Since the book was written in the Northern Wei Dynasty, no one has been able to solve this question for more than 300 years.
Wang Ou didn't expect Li Mu to be able to solve it. She just wanted to hit Li Mu and see how frustrated he was. She didn't know why she suddenly had such a bad taste. She knew clearly that she was not such a person. Maybe it was.
After seeing Li Mu's various surprises, I must have been confused.
After making up his mind, Wang Ou asked this question.
"Master Hou, the Nu family has also read the Sutra of Calculation. There is a question that the Nu family has not solved yet. I wonder if your algorithm can solve it?"
Li Mu didn't know what Wang Ou had in mind, thinking that she was still not convinced by his four arithmetic operations, so he said, "You tell me, I'll give it a try."
"There is a rooster, which is worth five; one hen, which is worth three; and three chickens, which are worth one. If you buy a hundred chickens for a hundred dollars, what are the roosters, hens, and chickens?"
"Hmm...is this a question?" Li Mu pondered for a moment, but he didn't feel the difficulty. He just felt strange. With the level of mathematics in the Tang Dynasty, had he already begun to study three-dimensional indefinite equations?
When Wang Ou saw Li Mu in trouble, he felt happy and finally managed to stump him!
"If it is too difficult, Lord Marquis, please don't calculate it. I am just curious. This question has been asked in ancient and modern times..." Wang Ou wanted to say that many arithmetic masters in ancient and modern times have not calculated this question. There is no shame in not being able to calculate it.
When I got there, I heard Li Mu say: "Four roosters, eighteen hens, and seventy-eight chickens. Or maybe there are only one rooster, eleven hens, and eighty-one chickens. Or there are twelve roosters."
, four hens and eighty-four chickens! Three answers in total!"
"Ah?" Wang Ou was completely stunned. Li Mu not only gave the answer, but also said three answers.
Seeing her in a daze, Li Mu felt proud and said, "If you don't believe it, you can verify it."
Of course Wang Ou wanted to verify. Li Mu had just taught her multiplication, so it didn't take long to verify. She only verified the first answer, and it was indeed correct. Suddenly she became a little autistic and looked at the numbers on the ground.