"The diameter is easy to say, but why is there a radius? It's because of the wheel, the wheel of the car."
"It is impossible to establish the concept of radius by just looking at the sun and moon, just looking at trees, just looking at people's eyes, etc."
"That's how it applies to mathematics."
"In other words, it can also be said that it is application that opens up mathematics, and it is also application that is constantly opening up and developing mathematics. There is no end to the times, and there is no end to application, so there is no end to mathematics."
Xu Guangling nodded.
Is there no end to his journey as a great master?
It should be.
But there is no need to discuss it if it is too far away, and it is meaningless to discuss it.
At the moment, his body and mind are always locked in the achievement of "knowledge aperture". Not to mention too far away, even the "heaven and earth aperture" after "knowledge aperture", Xu Guangling will not think about it for the time being.
If the knowledge acupoint is not achieved, the heaven and earth acupoints will be like castles in the air.
If you don't accumulate steps, you won't be able to reach a thousand miles.
The ancients regarded one step with one foot as a "step", and one step with each left and right foot as a complete "step". What Xu Guangling wants to do now, what he wants to do now, is to take steps from step to step and move forward steadily step by step.
Don’t be afraid of being slow, as long as you use both body and mind.
Don’t be afraid of being slow, just try your best.
Don't be afraid of being slow, as long as you keep walking 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 brilliant Milky Way, the spoon spindle, etc., they are all very beautiful. The world may not have the intention of art, but it does present beauty in a real way."
"Heaven and earth are like scrolls, and the avenues are like rafters and brushes."
"In this museum of heaven and earth, people first feel the beauty from each piece of art work, and then look down at the heaven and earth, and get deeper into its reality bit by bit."
“There is truth in beauty.”
"Taking our classical poetry as an example, it ranges from the four words of the Book of Songs in the Pre-Qin Dynasty to the five words of the Yuefu of the Han Dynasty, 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 rhythmic poems again, which are flat, flat, flat, flat, flat, flat."
"Rhythmic poetry was not prescribed by anyone, nor was it invented by anyone. When people looked at poems that had no particular rules in the past, they found that many poems, especially those by famous and great poets, actually conformed to such a rule.
"
"Different regions, different times, different people, different levels, and different moods write different poems. And in these poems, in statistics, we can find such a common pattern
.”
"What's the pattern?"
"It's the truth, it's the truth."
"Why stop at seven words? **Isn't ten words enough?"
"Why are there alternating between flat and oblique, and then there are so many complicated details within the framework of alternating between oblique and oblique?"
"Even to this day, we actually don't know."
"We only know that this is a kind of 'truth', a truth that has not yet been cracked."
"But whether we know it or not, whether it is broken or not, it does not prevent us from appreciating and feeling the beauty."
"This is the East."
"And in the West, I guess you must also know that very 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, there is such a kind of 'truth' and 'beauty' permeated in many places."
"We can make the inference that all artistic creations originate from truth and pursue beauty, and then in the process of pursuing beauty, unconsciously or consciously, they move towards a higher level of truth."
"Every great artist's creation must present beauty within truth, and truth must be contained within beauty."
Xu Guangling was thoughtful.
So in the future, when it comes to dabbling, at both ends of a certain scale, he will put mathematics on one end and poetry, music, painting, etc. on the other end? So that it is not ruled out that sometimes, he will use mathematics to study art, and use mathematics to study art.
An artistic way to study mathematics.
After a slight thought, Xu Guangling immediately thought of Bach's "Twelve Equal Temperaments".
"Let's talk about circles."
After a pause, Mr. Chen said slowly.
"The moon is round, the earth is round, the sun is round, 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 perfect circles, these are very complicated, and we are still unable to delve into their roots and essence. But there is one biggest reason why the tree trunks are not perfect circles."
Xu Guangling nodded, and then said: "The sun."
"Yes, the sun." Mr. Chen smiled, "Using the 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, or how the sun rises and falls, the tree's exposure to light will always be unequal, and its growth will also show an unequal trend."
"Under natural conditions, the faster the growth, the sparser the texture of the 'tree', the flatter it will be."
"Therefore, when the light is sufficient, we can judge the texture of the tree by its roundness. Similarly, we can also determine its latitude on the earth by the roundness of the tree."
"Trees at different latitudes in the north and south have different one-way expansion, or expansion coefficients, due to the different lighting conditions they receive."
"A single tree may have a large deviation, but if there are many trees together, the latitude can be accurately positioned."
Xu Guangling nodded.
"If a round thing is oppressed or restrained, it will become less round, or even not round at all."
“The moon, earth, and sun are like this, huge galaxies are like this, and things as small as a tree are like this.”
"The same is true for the human heart."
"What is the shape of human nature? It is invisible, but if it can be described, the innocent heart should be a perfect circle."
"As it gradually grows up, this perfect circle gradually changes. In our language, we use some words to describe people's character, such as gentleness, perseverance, extreme, etc., these are actually expressions
The difference in roundness.”
Xu Guangling pondered.
"I was walking on the road and saw a hundred dollars."
"To pick it up or not to pick it up?"
"Money is a good thing, I want to pick it up. This is my 'original intention'."
"Money is a good thing, but this money is not mine and should not be picked up. This is 'moral'."
"If I don't pick it up, others will pick it up, so it's better to give it to others than to me."
"If I don't pick it up, someone else will pick it up, so I picked it up and waited for the owner to hand it over to the management office, etc. But considering the actual situation,..."
"This is 'reality'."
"I'm very rich and I don't care about this at all, so I walked by indifferently."
"There are many more that could be listed."
"From the time a person is born, from childhood to adulthood, almost every moment, the human heart is faced with a similar situation, and then it swings left and right, uncertainly, and bit by bit, endures the pressure or pull from the outside world."
"Confucius has a saying, 'When I was fifteen, I was determined to learn; when I was thirty, I stood upright; when I was forty, I was not confused; when I was fifty, I knew the destiny of heaven; when I was sixty, I was attuned to my ears; when I was seventy, I did whatever I wanted without violating the rules.'"
"Do whatever you want without breaking the rules. This is actually two things."
"First do whatever you want."
"Then don't break the rules."
"Do whatever you want. It means to relax your heart internally and present the most natural state that is closest to a 'round' state."
"Not breaking the rules means externally, following the local customs and following the various requirements of the times, society, collectives, etc."
"Living a heart as close to a circle requires both cultivation and qualifications."
"That's a tall order."
Xu Guangling nodded.
Next, the course continues.
This class lasted about two hours.
From circles to hexagons, the shape of honeycombs, and the shape of a bunch of soap bubbles, and then from hexagons to triangles, and then to squares, Mr. Chen quoted extensively along the way and once again showed Xu Guangling the height and shape of his bulk.
Learn the breadth of five vehicles.
After two hours of class, just as Xu Guangling assigned homework to the two old people during this period, Mr. Chen also assigned a lot of homework to Xu Guangling. To use a certain Internet buzzword, it was, "Come on, let's do each other's homework."
It hurts!”
From "Zhou Bi Suan Jing" to "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 is a grand view.
After two hours of explaining the system, Mr. Chen assigned Xu Guangling a plan that would take more than two hundred hours and fill in a large amount of content in all aspects.
The next day, many mathematics books were delivered to the mountain.
As for Xu Guangling's reading content, in addition to the three categories of sages' books, Taoist canon, and farming books, there is another major category, mathematics.
==
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