Into Unscientific

  Chapter 24 This time and space, the only name!

  Outside the house.

  Looking at the calf who hurried back into the house, 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 looked along the situation, and saw Maverick was standing by the desk with a look of annoyance, his left hand clenched into a fist, and his knuckles were pressed heavily on the table.

  Obviously, Mavericks punched the desk deliberately.

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

  Xu Yun pretended to be stupid and stared at him again, and asked:

   "Math tool? Do you mean a ruler? Or a compass?"

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

   "Not a realistic tool, but a set of theories that can calculate rates 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 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 can understand, Yang Hui triangle."

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

   Maverick was originally talking according to his own thoughts, but he was taken aback when he heard Xu Yun's words clearly, then suddenly raised his head and stared at him firmly:

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

  Xu Yun thought for a while, then stretched out his hand to Mavericks:

   "Can 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 be rejected by Mavericks 100%.

   It is even possible to be sent another sentence, "You deserve it too?" '.

  But following the derivation of the dispersion phenomenon not long ago, Mavericks at this time has vaguely developed a slight interest in and recognition of 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 you don’t add it, 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", 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.

  So even with 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 .

   One 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 expression of the index score.

  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, then he can really sleep.

   Mavericks see dispersion phenomenon—Mavericks become curious—Mavericks calculates data—Mavericks thinks of stream counting—Xu Yun draws Yang Hui’s triangle.

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

  As for Xu Yun’s reason for drawing this picture is simple:

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

  Yang Hui's triangle was 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 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 in the graph is equal to the sum of two numbers C(n-1, r-1) and C(n-1, r) on its shoulder. "

   While talking, 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 power, Maverick's expression gradually became serious.

   But when Xu Yun wrote to the sixth power, Mavericks could not sit still.

   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 expressed the square root in such an intuitive way!

   More critically, the number m of 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 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 did 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 the problem of coefficients, but Mavericks' headache is the problem of indices.

   Now the Mavericks are like an old driver riding.

   Turning across a mountain road, I suddenly found a flat river 100 meters ahead. The scenery is magnificent, but there is a huge rockfall blocking the way more than ten meters in front of me.

   And just when the Mavericks were struggling, Xu Yun said another sentence slowly:

   "By the way, Mr. Newton, Sir Han Li has also studied the Yang-Hui Triangle.

   Later he discovered that the binomial exponent 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!"

  (end of this chapter)