Seeing the calf hurriedly running back into the house, Xu Yun vaguely realized something and followed quickly.
"Bang——"
As soon as he entered the house, Xu Yun heard the sound of a heavy object hitting him.
He looked over and saw that Maverick was standing by the desk with an annoyed look on his face, his left hand clenched into a fist and his knuckles pressed heavily on the table.
It was obvious that Mavericks had deliberately punched this desk just now.
Seeing this, Xu Yun stepped forward and asked:
"Mr. Newton, what are you..."
"You do not understand."
Mavericks waved his hands a little irritably, but within a few seconds he thought of something else:
"Feiyu, do you—or that Sir Han Li—know anything about mathematical tools?"
Xu Yun pretended to be stupid again and looked at him blankly and asked:
"Mathematical tools? You mean a ruler? Or a compass?"
Hearing these words, Maverick's heart immediately froze, but he couldn't stop like this after he had finished speaking, 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 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 continuously accumulated to calculate the product of the refraction angle.
For example, to multiply n a b, it 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 don’t think you understand it either.”
Xu Yun looked at him with a half-smile and said:
"I understand, Yang Hui's triangle."
"Well, so I'd better prepare to go to Uncle William later...wait, what did you say?"
Mavericks was originally speaking according to his own thoughts. After hearing Xu Yun's words, he was stunned. Then he suddenly raised his head and stared at him:
"Three stirs of sheep fat? What is that?"
Xu Yun thought for a while and stretched out his hand towards Mavericks:
"Can you pass me the pen, Mr. Newton?"
If this had been one day ago, when Mavericks had just met Xu Yun, Xu Yun's request would have been 100% rejected by Mavericks.
You may even be asked, ‘Are you worthy?’.
But with the recent derivation of the dispersion phenomenon, Mavericks now had a vague interest and recognition in Xu Yun - or in other words, Sir Han Li behind him.
Otherwise, he would not have explained so much to Xu Yunduo just now.
Therefore, facing Xu Yun's request, Mavericks rarely handed over the pen.
Xu Yun took the pen and quickly wrote a picture on the paper:
.............1
....... 1......1
....1......2......1
1.....3......3......1 (please ignore the ellipses, otherwise the starting point will be automatically indented, I'm confused)
.......
Xu Yun drew a total of eight lines. The outermost two numbers of each line were both 1, forming an equilateral triangle.
Friends who are familiar with this image should know that this is the famous Yang Hui triangle, also called Pascal's triangle - in the international mathematics community, the latter is more accepted.
But in fact, Yang Hui discovered this triangle more than 400 years earlier than Pascal:
Yang Hui was born in the Southern Song Dynasty. In his "Detailed Explanation of the Nine-Chapter Algorithm" in 1261, he preserved a precious diagram - the "Origin of Square Root Method" diagram, which is also the oldest existing triangular diagram with traces.
However, due to some well-known reasons, Pascal's triangle is much more widely spread, and some people don't even recognize the name Yang Hui's triangle at all.
Therefore, even with Yang Hui's original records, this mathematical triangle is still called Pascal's triangle.
But it’s worth mentioning…
Pascal studied this triangle diagram in 1654, and it was officially announced in late November 1665. Not long ago...
There’s still a whole month left!
This is why Xu Yun started with the dispersion phenomenon:
The dispersion phenomenon is a very typical differential model, even more classic than gravity. Whether it is the deflection angle or its "seven-in-one" appearance, it directly points to the calculus tool.
The concept of 1/7 is directly linked to the score of the index.
If Mavericks, who is exposed to the dispersion phenomenon, doesn't think about the 'Flux Technique' that he is at a loss for, he can just go to sleep.
Maverick saw the phenomenon of dispersion - Maverick became curious - Maverick calculated the data - Maverick thought of fluxes - Xu Yun introduced Yang Hui's triangle.
This is a perfect logical progression trap, a game 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 be named in someone else's name due to the grievances of modern times?
He had no control over the original time and space and had no ability to control it, but at this point in time, Xu Yun would not let Yang Hui Triangle share its name with Pascal!
With Mr. Niu as a guarantee, Yang Hui's triangle is Yang Hui's 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 remaining numbers are equal to the sum of the two numbers on its shoulders.
Any number C(n,r) illustrated graphically is equal to the sum of the two numbers C(n-1,r-1) and C(n-1,r) above it.”
As he spoke, Xu Yun wrote 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 cubic column, Maverick's expression gradually became serious.
But when Xu Yun wrote to the sixth power, Mavericks could no longer sit still.
He simply stood up, grabbed Xu Yun's pen, and started writing:
(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 Yang Hui's triangle have n terms, and the sum of the numbers is 2 raised to the n-1 power. The coefficients in the expansion of (a b) to the nth power correspond in turn to the (n 1)th row of Yang Hui's triangle.
Each!
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 that someone has expressed the square root in a graphic so intuitively!
More importantly, the m numbers 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 from n-1 different elements.
This is undoubtedly a huge help for 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 idea for him, but it does not help much with the problem he is currently stuck on, that is, the expansion of (P PQ)m/n.
Because Yang Hui's triangle involves coefficient issues, but Mavericks' headache is index issues.
Now Maverick is like an experienced rider.
When I turned a mountain road, I suddenly discovered that after a hundred meters in front of me, there was a flat river. The scenery was magnificent, but there was a huge pile of rocks blocking the road more than ten meters in front of me.
And just when Mavericks was struggling, Xu Yun said slowly:
"By the way, Mr. Newton, Sir Han Li has also done some research on Yang Hui's triangle.
Later he discovered that the exponent of the binomial did not necessarily need to be an integer, fractions and even negative numbers seemed feasible."
"He did not explain the argument method for negative numbers, but he left the argument method for fractions."
