Mr. Chen continued to tell.

"It's good to say that the diameter is good, but why is there a radius? because of the wheels of the car, the wheels of the car. ”

"You can't build the concept of radius by looking at the sun and the moon, by looking at the trees, by looking at the eyes of people, and so on. ”

"When it comes to mathematics, that's it. ”

In other words, it can also be said that it is the application that opens up mathematics, and it is also the application that constantly develops and develops mathematics. There is no end to the times, there is no end to the application, and there is no end to mathematics. ”

Xu Guangling nodded.

Is his path to a great grandmaster endless?

It should be.

But if it's too far away, it doesn't need to be discussed, and it doesn't make sense to talk about it.

At present, his body and mind are always locked in the achievement of "know-how". Don't say it's too far, even the "Heaven and Earth Know-how" after the "Know-how", Xu Guangling won't imagine it for the time being.

If there is no achievement, the heaven and earth are the towers in the sky.

No accumulation of steps, no thousands of miles.

The ancients took a step out of the foot as a "step", and the left and right feet each step as a complete "step", what Xu Guangling wants to do now, what he wants to do now, is to step by step, step by step and move forward steadily.

Don't be afraid of slowness, as long as you use both body and mind.

Don't be afraid to be slow, as long as you go all out.

Don't be afraid to be slow, as long as you always walk on this road.

"It has been said that there are only two universal languages in the universe, one is mathematics and the other is art. ”

"Mathematics is 'truth' and art is 'beauty'. ”

"There is beauty in truth. ”

"When we look at the starry sky at night, whether it is the brilliant Milky Way, or the spoon spindle, etc., it is very beautiful. Heaven and earth may not have a heart for art, but it is indeed a real way to present beauty. ”

"Heaven and earth are picture scrolls, and avenues are rafters. ”

"In this museum of heaven and earth, from the works of art, people first feel the beauty, and then look up to the heaven and earth, little by little, go deep into the truth. ”

"There is truth in the beauty. ”

"In terms of our classical poetry, from the four words of the pre-Qin poetry classic, to the five words of the Han Yuefu, then the six words of the Wei and Jin dynasties, and then the seven words of the Tang and Song dynasties. ”

After that, there were no more words, until seven. ”

And in the five or seven words, there is a rhyme poem, which is flat and flat, and is flat and flat. ”

"Lyric poetry is not prescribed by anyone, nor was it invented by anyone. People take a look at the poems that have not been elaborate in the past, and find that many poems, especially the poems of famous and great poets, actually conform to such a law. ”

"Different regions, different times, different people, different levels, and different moods write different poems. And then in these poems, in statistics, we can find such a common pattern. ”

"What's this pattern?"

"It's the truth, it's the truth. ”

"Why stop at seven words, **ten words?"

"Why is there a lot of complexity in the big framework of the level?"

"Even today, in fact, we don't know. ”

"All we know is that this is a 'truth', a truth that has not yet been deciphered. ”

But whether we know it or not, whether it is broken or not, it does not prevent us from appreciating and feeling the beauty in it. ”

"This is the East. ”

And in the West, you must also know the famous number in mathematics, 0.618. ”

Xu Guangling nodded.

"The golden section runs through mathematics and art, whether it is the artistic creation of heaven and earth, or the artistic creation of human beings, many places are permeated with such a kind of 'truth' and 'beauty'. ”

We can make such a presumption that all artistic creations originate from truth, the pursuit of beauty, and then, in the process of pursuing beauty, unconsciously or consciously, move towards a higher level of truth. ”

"In the creation of all great artists, beauty must be present in the truth, and there must be truth in the beauty. ”

Xu Guangling was thoughtful.

Therefore, in the future, when dabbling in the field, at both ends of a certain scale, he will put mathematics at one end, and poetry, music, painting, etc. at the other end?

With a slight movement in his thoughts, Xu Guangling immediately thought of Bach's "Twelve Equal Laws".

"Let's talk about the circle. ”

After a pause, Mr. Chen said slowly.

"The moon is round, the earth is round, the sun is round, and the trees are round. ”

"But we now know that these circles are not perfect circles. ”

"Why the stars are round and why they are not perfectly round, these are very complex, and we cannot go into its roots and essence yet, but there is one of the biggest reasons why the trunk is not perfectly round. ”

Xu Guangling nodded, and then said, "Sun." ”

"That's right, the sun. Mr. Chen smiled, "Using a tree as a reference, or from the standpoint of a tree, the sun always goes from east to west, not from south to north." ”

So no matter how the seasons change, no matter how the sun rises or falls, the degree of light exposure to the tree is always unequal, and then its growth also shows an unequal trend. ”

"In its natural state, the faster it grows and the more sparse the 'tree' is, the flatter it will be. ”

Therefore, in the case of sufficient light, we can judge the texture of the tree by its roundness. In the same way, we can also determine the latitude of a tree on Earth by its roundness. ”

"Trees at different latitudes in the north and south have different coefficients of unidirectional expansion or expansion because of the different light conditions they receive. ”

"A single tree may have a large deviation, but if it is a number of trees together, it is completely possible to accurately locate the latitude. ”

Xu Guangling nodded.

"A round thing, oppressed, restrained, will make it less round, even not round at all. ”

"This is true of the Moon, Earth, Sun, and huge galaxies, as small as a tree. ”

"The same is true of the human heart. ”

"What is the shape of the human mind? It is invisible, but if you describe it, the heart of a child should be perfectly round. ”

As it grows up, it gradually changes. In our language, some words are used to describe people's personalities, such as gentleness, perseverance, extremism, etc., in fact, they are all expressing the difference in roundness. ”

Xu Guangling pondered.

"Walking on the road, I saw a hundred dollars. ”

"To pick it up or not to pick it up?"

"Money is a good thing, want to pick it up. This is the 'heart'. ”

"Money is a good thing, but this money is not mine and should not be picked up. This is 'morality'. ”

"If I don't pick it up, it will be picked up by others, so it's better to be cheaper than to be cheaper for others. ”

"If I don't pick it up, someone else will pick it up, so I pick it up and wait for the owner, hand it over to the management office, etc., but considering the actual situation, ,......"

"It's 'reality'. ”

"I'm very rich, and I don't like this at all, so I walk by very indifferently and ignorantly. ”

"There are a lot to list. ”

"From birth, from childhood to adulthood, almost every moment, people's hearts are facing a similar situation, and then swaying from side to side, back and forth, in bits and pieces, under the pressure or traction of the outside world. ”

"Confucius has a saying, 'I have five out of ten and am determined to learn, thirty and stand, forty and not confused, fifty and know the destiny of heaven, sixty and obedient, seventy and do as I want without exceeding the rules.' ’”

"Do whatever you want and don't exceed the rules, these are actually two things. ”

"First of all, do what you want. ”

"And then it's not overstepping. ”

"To do what you want is to be inside, to stretch your heart, to present the most natural and closest to the 'circle' state. ”

"Not exceeding the rules, it is external, entering the countryside and following the customs, following the various requirements of the times, society, collective, etc. ”

"To live a heart as close to the circle as possible, this requires both cultivation and qualifications. ”

"That's a tall order. ”

Xu Guangling nodded.

Next, the course continues.

The lesson lasted about two hours.

From a circle to a hexagon, a honeycomb shape, and the shape of a bunch of soap bubbles, then from a hexagonal shape to a triangle, and then to a square, Mr. Chen once again showed Xu Guangling the height of his bulk and the breadth of his five cars.

After the two-hour class, just as Xu Guangling assigned homework for the two old men during this time, Mr. Chen also assigned a lot of homework for Xu Guangling, in a certain Internet buzzword, "Come on, hurt each other!"

From the Sutra of Arithmetic to the Nine Chapters of Arithmetic, from Pythagoras to the Fibonacci sequence, from the Pythagorean theorem, to Euler's formula......

There are all kinds of things, and there are big views.

After two hours of system explanation, Mr. Chen arranged for Xu Guangling, which required more than 200 hours of content and a lot of content to fill in.

The next day, a lot of math books were sent up the mountain.

In addition to the three categories of sage books, Taoist collections, and agricultural books, Xu Guangling's reading content has an additional category, mathematics.

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