Chapter 557 Truth and Beauty, Square and Circle

   Mr. Chen continued to speak.

   "The diameter is easy to say, why is there a radius? It's just because of the wheels, the wheels of the car."

   "It is impossible to establish the concept of radius by looking only at the sun and the moon, only at the trees, only at the eyes of people, etc."

   "Applied to mathematics, that is."

   "In other words, it can also be said that it is the application that has opened up mathematics, and it is also the application, which is constantly developing and developing mathematics. The times are endless, the application is endless, and the mathematics is endless."

   Xu Guangling nodded.

   His road to a great master is endless, isn't it?

should be.

   But there is no need to talk about it too far, and it is meaningless to talk about it.

   At the moment, his body and mind are always locked in the achievement of "knowledge". Don't say it too far, even the "Heaven and Earth Aperture" after "Knowing Aperture", Xu Guangling will not imagine the slightest bit of it for the time being.

   Knowing the aperture is not accomplished, the aperture of heaven and earth is a castle in the sky.

   If you don't accumulate a few steps, you can't go a thousand miles.

  The ancients used one step as a “sho”, and one step on each left and right foot as a complete “step”. What Xu Guangling has to do now, and what he wants to do now, is to walk steadily forward step by step.

   Don’t be afraid of slowness, as long as you use your body and mind together.

   Don’t be afraid of slowness, just go all out.

  Don't be afraid of slowness, as long as you always walk on this road.

   "Some people say 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 splendid Milky Way, the spoon spindle, etc., it is very beautiful. The heaven and earth may not have intentions of art, but it does present beauty in a real way."

   "Heaven and earth are the scrolls, and the avenues are the rafters."

   "In this museum of heaven and earth, from the works of art, people first feel the beauty, and then look down at the heaven and earth, and go deeper into the truth bit by bit."

   "There is truth in beauty."

   "As far as our classical poetry is concerned, from the four words of the Book of Songs in the Pre-Qin Dynasty, 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 are no more eight words, until seven."

   "And in the five or seven words, there are rhythm poems, which are flat and flat, flat and flat, flat and flat."

"The rhythm poems were not prescribed or invented by anyone. People looked at the previously indifferent poems and found that many poems, especially the poems of famous and great poets, actually conformed to such a law. "

"Different regions, different times, different people, different levels, and different moods, write different poems. Then, in these poems, in statistics, we can find such a common law ."

   "What is this law?"

   "It's the truth, it's the truth."

   "Why stop at seven words, can't eighty or ninety words be enough?"

   "Why are flat and flat, and then there are a lot of complicated details under the big framework of flat and flat?"

   "Even to this day, in fact, we don't know it."

   "We only know 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."

   "In the West, you must also know a very famous number in mathematics, 0.618."

   Xu Guangling nodded.

   "The golden section runs through mathematics as well as 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, pursue beauty, and in the process of pursuing beauty, unconsciously or consciously, move towards a higher level of truth."

   "Every great artist's creations must show beauty in truth, and beauty must contain truth."

   Xu Guangling was thoughtful.

   So in the future, when he is dabbling, at two ends of a certain scale, he wants to put mathematics at one end, and poetry, music, painting, etc. at the other end? So that it cannot be ruled out that at some point, the mathematical method is used to study art, and the artistic method is used to study mathematics.

   Thoughts moved slightly, Xu Guangling immediately thought of Bach's "The Twelve Average Laws".

   "Let's still talk about circles."

  After a pause, Mr. Chen said slowly.

   "The moon is round, the earth is round, the sun is round, and the tree is round."

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

   "Why the stars are round and why they are not perfect circles, these are very complicated, and we can't go deep into its roots and essence yet, but there is one biggest reason why the trunk is not perfectly round."

  Xu Guangling nodded, then said, "The sun."

   "Yes, the sun." Mr. Chen smiled. "With 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, and no matter how the sun rises or falls, the tree's exposure to light is always unequal, and then its growth also shows an unequal trend."

   "In the natural state, the faster the growth and the sparser the texture of the 'tree', the flatter it will be."

   "Therefore, in the case of sufficient light, we can completely judge the texture of the tree by the roundness of the tree. Similarly, we can also determine its latitude on the earth by the roundness of the tree."

   "Trees with different latitudes in the north and south have different lighting conditions, so their one-way expansion or expansion coefficients are different."

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

   Xu Guangling nodded.

   "A round thing, when oppressed or restrained, will make it not so round, or even completely unround."

   "The moon, the earth, and the sun are so, so are the vast galaxies, as small as a tree."

   "The human heart, too."

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

"As it grows up, it is perfectly round, and it gradually changes. In our language, some words are used to describe people's characters, such as gentleness, perseverance, extremeness, etc., all of which are actually expressing The difference in roundness.”

   Xu Guangling pondered.

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

   "To pick up or not to pick up?"

   "Money is a good thing, I want to pick it up. This is the 'true 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, others will pick it up, so it's better to be cheap to others than to be cheap to me."

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

   "This is 'reality'."

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

   "There are many more to list."

   "From birth, from childhood to adulthood, almost every moment, the human heart is faced with a similar situation, and then swaying from side to side, uncertain back and forth, bit by bit, under external pressure or traction."

   "Confucius has a saying, 'At fifteen I set my mind on learning, at thirty I stand up, at forty I have no doubts, at fifty I know the mandate of heaven, at sixty my ears are obedient, at seventy I can do whatever I want without breaking the rules.'"

   "Do whatever you want without breaking the rules. These are actually two things."

   "First do whatever you want."

   "Then it's not breaking the rules."

   "Do whatever you want, it is inside, let the heart stretch and present the most natural and closest state of 'round'."

   "Don't go beyond the norm, you are outside, you go to the countryside and follow the customs, and follow the various requirements of the times, society, collectives, etc. for people."

   "To live a heart as close to a circle as possible requires both self-cultivation and qualifications."

   "That's a tall order."

   Xu Guangling nodded.

   Next, the lesson continues.

   This class lasted about two hours.

From circle to hexagon, the shape of a honeycomb, and the shape of a pile of soap bubbles, and then from hexagon to triangle, and then to square, Mr. Chen has been widely cited along the way, and once again showed Xu Guangling its large height and Learn the breadth of the five cars.

After two hours of class, just like Xu Guangling assigned homework for the two old people during this time, Mr. Chen also assigned a lot of homework for Xu Guangling. To use a certain Internet catchphrase, it is exactly, "Come on, let's talk to each other. Hurt!"

  From "Zhou Bi Suanjing" to "Nine Chapters of Arithmetic", from Pythagoras, to Fibonacci sequence, from Pythagorean theorem, to Euler's formula...

   There are many, many grand views.

  After the two-hour system explanation, Mr. Chen arranged for Xu Guangling, which may take more than two hundred hours, and a lot of content to fill.

   The next day, many math books were sent up the mountain.

   Xu Guangling's reading content, in addition to the three categories of sages, Taoist books, and farming books, has another major category, mathematics.

  ==

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   (end of this chapter)