Into Unscientific

outside the house.

Seeing the calf running back into the house in a hurry, Xu Yun vaguely realized something, and followed quickly.

"Boom—"

As soon as he entered the room, Xu Yun heard the sound of a heavy object hitting.

He followed the trend, and saw that Maverick was standing by the desk with an annoyed expression on his face, his left hand was clenched into a fist, and his knuckles were pressing heavily on the desk.

Obviously, the Mavericks punched the desk deliberately just now.

Seeing this, Xu Yun stepped forward and asked:

"Mr. Newton, this is."

"You do not understand."

Maverick waved his hand a little irritably, but within a few seconds he thought of something again:

"Fat Yu, do you—or that Sir Han Li, know about mathematical tools?"

Xu Yun looked at him again pretending to be a fool, and asked:

"A math tool? Do you mean a ruler? Or a compass?"

Hearing these words, Maverick's heart immediately turned half cold, but he couldn't stop like this halfway through, so he continued:

"Not a realistic tool, but a set of theories that can calculate the rate of change.

For example, the dispersion phenomenon just now is an instantaneous rate of change, and it may even involve some particles that cannot be seen by the naked eye.

To calculate this rate of change, we need to use another tool that can be accumulated continuously to calculate the product of refraction angles.

For example, the multiplication of n a+b is to take the product of a letter a or b from a+b, for example (a+b)^2=a^2+2ab+b^2 forget it, I guess you also listen don't know. "

Xu Yun glanced at him with a half-smile, and said:

"I understand, Yang Hui Triangle."

"Well, so I'm going to wait a while, Uncle William. Wait, what did you say?"

Xiao Niu was originally talking according to his own thoughts, but when he heard Xu Yun's words, he was taken aback for a moment, then suddenly raised his head, staring at him firmly:

"Three stirs of sheep fat? What is that?"

Xu Yun thought for a while, then reached out to Mavericks:

"Could you pass me the pen, Mr. Newton?"

If it was a day ago, that is, when Xiao Niu first met Xu Yun, Xu Yun's request would have been rejected by Maverick 100%.

There may even be another sentence, "You deserve it too?" '.

But following the deduction of the dispersion phenomenon not long ago, Mavericks at this time has vaguely developed a sliver of interest and recognition for Xu Yun—or the Sir Han Li behind him.

Otherwise, he wouldn't have explained what he said to Xu Yunduo just now.

Therefore, in the face of Xu Yun's request, Mavericks handed out the pen in a rare way.

Xu Yun took the pen and quickly drew a picture on the paper:

1

11

121

1331 (please ignore the ellipsis, if not added, the starting point will be automatically indented, dizzy)

Xu Yun drew a total of eight lines, and the outermost two numbers in each line are both 1, forming an equilateral triangle.

Friends who are familiar with this image should know that this is the famous Yanghui triangle, also known as Pascal's triangle - in the international mathematics community, the latter is more accepted.

But in fact, Yang Hui discovered that the year of this triangle is more than 400 years earlier than Pascal:

Yang Hui was born in the Southern Song Dynasty. In his "Detailed Explanation of the Nine Chapters Algorithm" in 1261, he preserved a precious graph - the "Origin of Prescribing Method" graph, which is also the oldest existing triangular graph with traces.

However, due to some well-known reasons, the spread of Pascal's triangle is much wider, and some people don't even recognize the name of Yang Hui's triangle.

Therefore, despite Yang Hui's original records, this mathematical triangle is still called Pascal's triangle.

But it's worth mentioning that.

Pascal studied this triangular diagram in 1654, and it was officially published in late November 1665, which is now .

There is a full month left!

This is also the reason why Xu Yun started from the phenomenon of dispersion:

Dispersion phenomenon is a very typical differential model, even more classic than gravitation. Whether it is the deflection angle or its own "seven-in-one" appearance, it directly points to the calculus tool.

The concept of 1/7 is directly linked to the index's score statement.

If the Maverick who has been exposed to the phenomenon of dispersion does not think of the 'flux technique' that he is unable to do anything about, then he can really sleep well.

Mavericks sees the phenomenon of dispersion——Mavericks becomes curious——Mavericks calculates data——Mavericks thinks of flow counting——Xu Yun draws Yang Hui's triangle.

This is a perfect logical progressive trap, a bureau from physics to mathematics.

The reason why Xu Yun drew this picture is very simple:

Yang Hui's triangle is a thorn in the heart of every mathematics practitioner!

Yang Hui's triangle is originally a mathematical tool invented by our ancestors and has conclusive evidence. Why is it forced to hang under the name of others because of modern aggrieved reasons?

He has no control over the original space-time and has no ability to control it, but at this point in time, Xu Yun will not let Yang Hui's triangle share his name with Pascal!

With Mr. Niu as a guarantee, the Yanghui triangle is the Yanghui triangle.

A term that only belongs to China!

Then Xu Yun let out a deep breath, and continued to draw a few lines on it:

"Mr. Newton, you see, the two hypotenuses of this triangle are composed of the number 1, and the rest of the numbers are equal to the addition of the two numbers on its shoulder.

Any number C(n, r) illustrated on the graph is equal to the sum of two numbers C(n-1, r-1) and C(n-1, r) on its shoulder. "

As he spoke, Xu Yun wrote down a formula on the paper:

C(n, r)=C(n-1, r-1)+C(n-1, r) (n=1, 2, 3,...n)

as well as

(a + b)^2 = a^2 + 2ab + b^2

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

(a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 6ab^3 + b^4

(a + b)^5 = a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5

When Xu Yun wrote the column of the third square, Maverick's expression gradually became serious.

But when Xu Yun wrote to the sixth power, Mavericks couldn't sit still.

He simply stood up, grabbed Xu Yun's pen, and wrote by himself:

(a + b)^6 = a^6 + 6a^5b + 15a^4b^2 + 20a^3b^3 + 15a^2b^4 + 6ab^5 + a^6!

It is clear.

The numbers in the nth row of Yanghui's triangle have n items, and the sum of the numbers is the n-1 power of 2, and the coefficients in the expansion formula of the nth power of (a+b) correspond to the (n+1)th of Yanghui's triangle in turn Every item in the row!

Although this expansion is not difficult for Mavericks, it can even be regarded as the basic operation of binomial expansion.

However, this is the first time someone has graphically expressed the root number so intuitively!

More importantly, the m number in the nth row of Yang Hui's triangle can be expressed as C(n-1, m-1), which is the number of combinations of m-1 elements taken from n-1 different elements.

This is undoubtedly a huge boost to Mavericks' ongoing binomial derivation!

but

Maverick's brows gradually wrinkled again:

The emergence of Yang Hui's triangle can be said to have opened up a new way of thinking for him, but it does not help much with the problem he is currently stuck on, that is, the development of (P+PQ) m/n.

Because what Yang Hui's triangle involves is the coefficient problem, but what Mavericks has a headache is the index problem.

Now the Mavericks are like an old driver riding.

When turning around a mountain road, I suddenly found that there was a flat river 100 meters ahead, and the scenery was magnificent, but there was a huge rockfall blocking the way more than ten meters ahead.

And just when Maverick was struggling, Xu Yun said slowly:

"By the way, Mr. Newton, Sir Han Li has also done research on Yang Hui's triangle.

Later he discovered that the exponent of the binomial does not necessarily need to be an integer, and fractions and even negative numbers seem to be feasible. "

"He didn't explain the argumentation method for negative numbers, but he left the argumentation method for fractions."

"he called it"

"Han Li unfolds!"