My younger brother Zhuge Liang

Chapter 41 How can Aliang be so worthy of the title? How dare he underestimate the wise men in the world?

After Zhuge Liang finished writing his reply, he went to the back room and handed the first volume of his brother's letters to his eldest sister Zhuge Zhi and second sister Zhuge Lan, who had just finished washing the dishes and clothes.

Zhuge Zhi is already nineteen years old. If she hadn't been displaced and had no place to settle down, she would have been considered an old leftover woman if she hadn't married at this age.

Zhuge Lan is seventeen years old and the pressure is not much less.

A few months ago, they also secretly observed Kuai Qi, Pang Shanmin and others who came to visit.

But Kuai Qi was really a fool, just from a distinguished family, because the Kuai family was now the number one civil official family in Jingzhou. Zhuge Zhi was very dissatisfied with him, but he also had a sense of self-sacrifice in his heart.

As for Pang Shanmin, his knowledge and character are better than Kuai Qi, after all, he is Pang Tong's cousin. But his appearance is even more rustic, which is really unsightly. After all, Zhuge Lan has her elder sister to protect her, and sometimes she thinks: If her elder sister sacrifices, then she won't have to sacrifice herself... Isn't the Kuai family enough to protect the Zhuge family?
So, just now before dinner, when they heard their third brother quietly saying that their eldest brother had suddenly become rich in Guangling, and was treated as a teacher by the General Zhendong, and had also brought him countless treasures, the depressed Zhuge Zhi and Zhuge Lan instantly breathed a sigh of relief.

"Big brother has suddenly become so powerful? Then do we not have to live under someone else's roof and rely on marriage to gain status?" This was the first reaction of the two sisters. They imagined that if the big brother's situation could be better than that of their uncle, they would decisively go to him for help!
Even if I want to get married in the future, I want to marry a handsome man. I don’t have to sacrifice my character and appearance for money, power and status.

Now that they saw that their second brother had finally finished reading the letter and written a reply, they came over eagerly to read it together.

Zhuge Jin's confident writing style also seemed unfamiliar to them.

"Brother used to be so modest even when writing home, but now he is so domineering as Mencius, who else can do it better than me? The change is so great, it shows that he has really made great progress." Zhuge Zhi is the closest in age to Zhuge Jin and knows him best, so she couldn't help but praise him.

Zhuge Lan looked at him for a while, then pushed his second brother and said, "Aliang! If big brother can really protect us, my sister and I will go there first, and you stay in Jingzhou and mediate with the young lady from the Huang family.

Anyway, you men should just marry a wife for her virtue. If you are not satisfied with her beauty, you can still have the opportunity to take concubines in the future. We only have one chance, so I will not accompany you."

Zhuge Lan had also met Huang Yueying and knew that his second brother got along well with her - of course, they were just ordinary friends.

The girl had good character and knowledge, but she was not fair and pretty enough, and her hair was not shiny black. It was obvious that she was weak in both energy and blood, and her internal energy was insufficient.

Zhuge Lan felt that compared to what happened to her and her elder sister, her second brother's situation was acceptable. After all, they had similar interests, and it would not be too late to take a concubine or find a beautiful woman in the future.

Zhuge Liang originally wanted to analyze his eldest brother's changes with his elder and second sisters, but Zhuge Lan's words made him anxious. He dropped the letter and turned away, returning to his room to study the secret scroll given to him by his eldest brother.

……

After all, Zhuge Liang was only sixteen years old, and boys are often not as precocious as girls of the same age, so he felt a little embarrassed when his second sister teased and bullied him about his friendship with Huang Yueying.

At times like this, doing exercises is the best way to divert attention! He opened his brother's second scroll and began to study it.

"I want to see what progress Big Brother has made in the past two years. He actually feels that he can teach me. Could it be that he has found some obscure knowledge..."

Zhuge Liang quickly scanned it and found that the first half of the second volume was mainly a table of contents, which summarized the contents of the subsequent dozen volumes and made an index.

The second half is a reflection on the experience of encouraging learning, mainly discussing the mentality and other major principles of studying.

Zhuge Liang curled his lips. What he needed now was a challenge! He wanted to practice questions to relieve the embarrassment! He didn't want to read the same old stuff for the time being!

As for the study method, can the elder brother's study method be better than mine? If he had this ability, he would not have been crushed by me back then.

So Zhuge Liang dropped the second volume and skipped it directly, just following the table of contents and jumping through volumes five to eight.

The catalog says that these four volumes are all about mathematics! They are more profound and comprehensive than "Zhou Bi" and "Jiu Zhang".

Zhuge Liang knew very well that when he left his hometown two years ago, his mathematics skills were definitely better than his elder brother's.

Then let’s first take a look at how much weight these things that Big Brother considers to be good things actually have.

……

"Huh? What the hell is this?"

It’s no wonder, as soon as Zhuge Liang opened the fifth volume, he was really shocked by the first impression.

Because he didn't recognize any of the scribbles on the scroll.

Fortunately, his desire to explore was stable. He took a deep breath and read on carefully without fear. Sure enough, every symbol had an explanation before being used.

"Ha! So it's just Sindhu numbers and symbols. The purpose is to omit the words 'ten, hundred, thousand, and ten thousand' and directly use the digits to represent ten, hundred, thousand, and ten thousand. It saves a lot of effort... It also makes it easier to use symbolic formulas directly, which is much easier than using words to describe the algorithm."

Zhuge Liang spent a cup of tea to first accept the Arabic numerals 0 to 9, and spent another cup of tea to accept the "+-×÷/=" signs. He also took a piece of wood and practiced writing each dozens of times with a gray pen. Then he realized the labor-saving effect of this thing. After mastering the numbers and symbols, he looked at the first few questions listed by his elder brother for him to adapt to, and Zhuge Liang quickly regained his confidence.

"Isn't this just a restatement of the Nine Chapters of Chickens and Rabbits in the Same Cage using Sindhu numbers and formulas? Why are there X and Y... Hmm, it seems that these two runes mean A, B, and C, and in this question they represent the number of chickens and rabbits respectively..."

"This one uses the Sindhu formula to express the hypotenuse of three, the leg of four, and the length of five. It's nothing new, but the idea of using a special symbol to substitute into the formula does simplify it a lot. I don't have to think about the meaning every time. I just have to deal with numbers..."

In just two questions, Zhuge Liang summarized the main benefits of using numbers and symbols, and a spark of "mathematical abstraction" was also ignited in his heart.

The traditional Zhoubi and Jiuzhang were too application-oriented, and their generalization and abstraction of mathematics were definitely not as good as those of later generations. Zhuge Jin only sorted it out and restated it, which made his second brother's way of thinking improve.

After the ancients finished learning Zhoubi, they were roughly equivalent to the level of fourth or fifth graders in later generations, that is, the four arithmetic operations, fractions, negative numbers, and the calculation of the perimeter and area of simple figures.

After learning "Nine Chapters", one can roughly reach the level of junior high school mathematics in later generations, including the Pythagorean theorem and various multivariate linear equations. However, it lacks circular geometry, square roots, and irrational numbers compared to later generations.

It took Zhuge Liang only half an hour to understand all the mathematics up to the first grade of junior high school again, and it was very easy.

"Brother, you underestimate my foundation! However, he can also understand these. It seems that he has made great progress in the past two years." Zhuge Liang thought proudly.

He continued to read on with courage and diligence. The second half of the fifth volume was about something called "the method of cutting a circle", as well as the derivation of the principles of area calculation for other complex geometric figures.

Zhuge Jin wrote the article in great detail and gave the conclusion at the end. It was not like later textbooks that lacked the proof process of basic formulas and directly asked students to memorize them.

Such a lesson plan that is easy to understand and has clear logic is difficult to write on one's own unless one is a top-notch lecturer.

"Hmm? That's interesting. I never thought that if you stretch a circle infinitely, it will become countless triangles with the perimeter as the total base length... And this kind of odd-shaped pattern can also be cut, patched and converted to deduce the area calculation method. It will definitely be useful when measuring acres of land in the future. I don't have to walk every row step by step."

Zhuge Liang's mood finally changed from the initial surprise to a slightly solemn one.

This time it took him more than an hour to finally understand it thoroughly.

After doing all this, when he came back to his senses from his intoxication, he found that the simple clepsydra on the desk had already stopped ticking.

It was a dark night at the beginning of the month. I didn't know what time it was. Maybe it was the hour of the dog? Everything was quiet. My sisters and my third brother had already fallen asleep.

Zhuge Liang still couldn't contain his excitement and went to get the sixth volume.

This volume begins with the principle of square root, trigonometric functions, and the irrational numbers derived from them - of course, Zhuge Jin used experimental methods to demonstrate this, rather than purely mathematical methods.

I won't go into details, but it is a very step-by-step process and very suitable for Zhuge Liang's current knowledge structure.

Trigonometric functions and square roots are still closely followed by the generalization of the integer solutions to the Pythagorean theorem in the fifth volume, and are inspired step by step. The thread is very clear.

After making up for these two shortcomings, Zhuge Liang was able to completely surpass the mathematical level of later first-year junior high school students, and began to get a glimpse of the "trigonometric functions" of higher grades.

But this time Zhuge Liang finally suffered the consequences.

He looked at it for another half a quarter of an hour, but still didn't know how to calculate it.

He really wanted to do an experiment. He would cut and make so many triangular wooden boards with specific angles according to the method shown by his elder brother, and then use a ruler to measure the specific length of the hypotenuse to obtain the function value and square root number.

But it was already late at night, and they didn't want to make too much noise. They also couldn't find tools or materials, so they had to give up.

At this moment, Zhuge Liang finally put aside his contempt for mathematics.

"Big brother must have had some adventures in the past two years!" Looking at the completely incomprehensible contents in the sixth volume, and the seventh and eighth volumes that were like a heavenly book, he finally realized his position.

"The third and fourth volumes are about the basics of logic and common sense. Volumes nine to eleven are about the principles of nature. Volumes twelve to fourteen are about the principles of agriculture and animal husbandry. Volumes fifteen and sixteen are about the application of craftsmanship... It actually covers such a wide range. Did I underestimate what Big Brother had learned at the beginning? I shouldn't have skipped ahead just now."

After going through all the catalogs, Zhuge Liang finally adjusted his attitude and decided to take back his elder brother's original "Encouragement to Study" and read it carefully from the beginning. Perhaps that would achieve twice the result with half the effort and avoid the problem of "haste makes waste".

He opened the second volume that he had thrown aside and began to read it with a pious and calm mood without a trace of arrogance.

Perhaps, this was one of the rare times in Zhuge Liang's life when he put aside his "general idea" and worked hard to "achieve perfection".

(End of this chapter)