Shen Lang's sentence shows the charm of mathematics, although many things can be calculated by computers to calculate the final answer, but computers are always just computers, and the human brain is the most complex calculation program.

It is through the human brain that it is possible to solve the world's complex mathematical problems that have not been solved until now.

Even if it may be a long time, it will be solved one by one in the end.

"How? In the past few days, what do you not understand? ”

In beauty and mathematics, Shen Lang perfectly integrates the two, no one delays anyone, when it comes to beauties, he is professional, when it comes to mathematics, he is also erudite, if Shen Lang was born in the Ming Dynasty, I am afraid that he will be a merry genius like Tang Bohu, of course, the premise is that the Ming Dynasty is also good at mathematics, not literature.

When Fang Chao heard this, he immediately told him what he didn't understand in the past few days, hoping to get Shen Lang's guidance.

Shen Lang's curiosity for Fang Chao, but as long as he can say it, he will not hesitate to give advice, willing to share things, he has taken a fancy to Fang Chao's potential, and regards him as his junior, hoping that Fang Chao's level in mathematics can be greatly improved.

Chinese people can't say that there is little research in mathematics, but when it comes to the professional field, there are very few mathematical geniuses of the younger generation, and the older generation is unwilling to teach more, just throw some templates and papers to you and let you understand it yourself.

How much you can comprehend depends on your personal ability.

After all, mathematics is not easy to teach, especially advanced mathematics, if you have no talent, even the teacher is unwilling to say a few more words, it is too wasteful.

If he really has a certain talent in mathematics, in terms of Shen Lang's temperament, he may not say a few words, and his current approach is the same as that of some older professors, and he is very high-minded.

But Fang Chao is really an exception, such a person, Shen Lang is trying his best to let Fang Chao go to Qingbei University, in this way, with such a junior, he will be very happy, and he is willing to spend more time on Fang Chao, because no matter how much effort is spent, Fang Chao is from the Qingbei Department......

But if Fang Chao finally decides to go to Peking University, isn't this tantamount to raising tigers? Set up a formidable enemy for Qingbei?

But in the end, Shen Lang discarded this absurd idea, what Qingbei and Peking University, everyone is Chinese, isn't it good to let the Chinese have a strong mathematician?

Besides, Fang Chao's comprehension ability is so strong, just pointing out the other party's mathematics will greatly improve, why not do it?

So Fang Chao took out a useless piece of waste paper from the ground, and then took out the hotel's ballpoint pen and wrote a line of number symbols on it.

There are two n-dimensional vectors, (X1, X2, X3...... Xn）、（Y1，Y2，Y3…… Yn）。

Define its inner product, =X1· Y1+X2· Y2+X3· Y3+…… Xn· Yn

"Now that we have a definition, we can define two more concepts, distance and orthogonality, to define the norm as...... The corresponding distance can be defined as...... The two vectors X and Y are orthogonal if ......"

While speaking, Fang Chao quickly wrote down a few formulas on scratch paper.

|X|=√（X，X）

d（X，Y）=||X-Y||

=0

"Suppose there are n vectors, E1, E2, E3...... En, and satisfies =0, then these n vectors form an orthogonal basis, i.e., ||Ei||=1, now define Ai=, we get X=Ea,A=(A1,A2,A3...... An），E=（E1，E2，E3…… En）。 ”

"Then the coordinates in the coordinate system are composed of these data, then ......"

Fang Chao was still writing the data, but Shen Lang immediately knew where Fang Chao's doubts were, and immediately said directly, "Chao'er, why don't you try to use the Fourier series?" ”

"it!"

"yes, why didn't I think of using Fourier series? Brother Lang, you are simply a god! ”

The big guy deserves to be the big guy!

Great God Shen Lang knew where his confusion was before his problem was completely formed, which was not something that ordinary people could do......

Originally, Fang Chao was somewhat blocked, such as a huge stone appeared on a road, Fang Chao was still hesitating whether to bypass it or find a way to move the stone, because this stone was so coincidental, the place where it appeared was very unusual, if the word was bypassed here, then it would also appear in other places, like a lonely ghost, haunting you, always ghostly.

But Shen Lang came out, he used the Fourier series, it is like a 'swastika' character, suppressing the dead ghost, so that it has no way to trap you all the time, and now you only need you to take action, you can kill its soul, or even crush the bones and ashes.

"Chao'er, we now think of any function as a vector, let's find a set of functions, for example, sin(nx), cos(mx) then ......"

Shen Lang picked up a piece of scratch paper from the ground at random, and then took out a pen from his jacket pocket, and then wrote on the paper.

Between 0~2π of the function.

sin（nx）cos（mx）dx=0

cos（mx）cos（nx）dx=0，n≠m

sin（nx）sin（mx）dx=0，n≠m

"Chao'er, what did you think of?"

Fang Chao looked at the function written by Shen Lang, and at the same time connected to the Fourier series, he didn't think about it and said, "Inner product." ”

The communication between the top students is so simple, the two of them can say anything a little bit, Shen Lang just likes this, the only thing he loves in his life is two things, beauty and mathematics.

People don't need to pursue too much in this life, just be fine.

Shen Lang felt that he was okay, so he liked two things, and he could like them for a lifetime.

If you are a beauty, he can talk freely with any beauty, astronomy and geography, and even some sassy words.

Mathematics alone is sacred, and cannot be explored and discussed in bed.

And now, he found the person who could talk about mathematics with him, although Fang Chao is still young, but he is very malleable and talented, it won't be long before Fang Chao may catch up with him, thinking of having a rising star, and even making him thrive because of some of his help, Shen Lang has a sense of pride in his heart.

"That's right, it's the inner product, then the above sin cos function becomes a set of orthogonal bases, and then take a closer look at the formula of the Fourier series, the Fourier series is nothing more than projecting a function onto this orthogonal basis. So the Fourier series is really just a set of "coordinates". ”

"Of course, this coordinate is infinitely dimensional......"

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