Lord of the Desert

Chapter 38 Taylor Unfolds
"How could you know the circumference ratio calculated in the prison?"

Zhao Feng'er fell down, but he didn't care about the pain, and quickly got up to question.

"It shouldn't be. Although the secret level of this secret is not very high, it shouldn't be known to outsiders..."

But he still misses the point.

"No, Jing Fu, the micro number he just mentioned is not eleven, but thirteen!"

The big head pulled off his companion's arm and added.

Only then did the person called "Jingfu" realize that the number reported by the young master of the Hong family on the opposite side was two more than that of Qi Zuojian!
Although the number may not be correct, but the first eleven can be matched, which is enough to make the two of them awe-inspiring.

"No, young master, you have to follow me back to meet the master!"

Regardless of his low cultivation level, he came up and grabbed Hong Fan's sleeve, and said awe-inspiringly.

The latter of course will not refuse.

Hong Fan originally used this to seek advancement.

A quarter of an hour later, Jin Haicheng was in prison.

In the main hall, the master craftsman Wen Zhongguan is holding a thinned cloth charcoal pen, writing and drawing on the paper.

But a clatter of footsteps from outside interrupted him.

Master Wen looked up and saw his two disciples Jia Ziyong and Zhu Jingfu trotting in, followed by a handsome young man.

"Teacher, the disciple has a big report!"

As soon as he got started, Zhao Fenger Zhu Jingfu yelled.

"This young man, he, cough cough..."

Because the words were too hasty, he choked on his own saliva before he finished speaking.

"Sit down and talk about it, what does it look like?"

Wen Zhongguan let out a low shout, and immediately killed the eagerness of the two disciples.

At this time, Hong Fan was also secretly looking at the sixth-rank official, Jin Haiqi, who was at the same level as Cheng Juan Hongwu, as the head of the prison.

He is short and stocky, with eyes like copper bells and thick joints.

Although she was wearing a literary robe, she exuded a bandit air.

"Teacher, this Mr. Hong Fan claims to have calculated pi with thirteen digits."

After calming down his cough, Zhu Jingfu said.

Wen Zhong Guan heard the words, his complexion remained unchanged, the corners of his mouth were slightly pursed, seemingly disdainful.

But what Jia Ziyong said next made him no longer calm down: "And the first eleven are all in line with the calculations in our prison."

"Is this true?!"

Wen Zhongguan asked in a low voice, looking at Hong Fan with piercing eyes.

The latter leaned back and smiled, and immediately recited the thirteen-digit pi again.

For a while, the main hall fell into silence.

"Xiao Zhu, Xiao Jia, you must have accidentally revealed the secret rate!"

At this time, a reproach came from the side door.

Hong Fan turned his head and saw a tall, thin middle-aged man with a mustache walking in.

"Master, you have wronged us!"

Seeing this person, Zhu and Jia immediately stood up and replied.

[The master craftsman is the sixth grade, and the master is the eighth grade; this person should be Wen Zhongguan's deputy. 】

Hong Fan thought about it in his heart, and then opened his mouth to defend himself.

"The two lords have clearly noticed that I did not know Zhu Jia before today."

"As for the thirteen-digit pi, I calculated it independently."

"Independent calculation?"

But his words made the tall and thin master sneer even more.

"Then let me ask you, where did you get the algorithm? How long did it take you to calculate such an accurate number?"

"I think you are at most seventeen or eighteen years old, and you obviously still have martial arts skills. You can't say that you are all on your own, right?"

Even in Hong Fan's view, this person's doubts are reasonable.

In his previous life, he himself would not have believed that an individual could create results beyond the mainstream academia by relying solely on independent deduction from scratch.

But who made the traverser stand on the shoulders of countless giants?

"Reporting to Your Excellency, I figured out the algorithm myself; the calculation of the thirteen digits was easy, and it didn't take much time."

Hong Fan cupped his hands slightly, and spoke boldly.

This time, even Wen Zhongguan, who had been noncommittal, showed impatience.

But before several people spoke, Hong Fan spoke again.

"I know a few people who use circumcision to calculate pi."

"In my opinion, this method is too primitive, complicated and inefficient."

His tone was sincere, but his words were offensive.

"presumptuous!"

The tall and thin master suddenly changed his face, and cursed.

"Qian Hong, be safe and don't be impatient."

Wen Zhongguan waved his hand, signaling his deputy to appease his anger.

"The circle-cutting technique is primitive? Mr. Hong has a serious tone."

He raised his hands and stared at the young man with piercing eyes.

"Now that I have paper and pen, why don't I wait to see what your Excellency does?"

"Just do what you want, don't dare to ask your ears!"

Hong Fan immediately agreed, stepped forward to hold the charcoal pencil, and flipped the half-written paper of Wen Zhongguan to the ground, revealing the white paper underneath.

Then, according to the mathematical knowledge in his previous life, he started from the definition of the derivative, and wrote down the complete derivation process of Taylor's formula.

For a while, there were only the sound of wind, breathing, and the rustling of charcoal writing in the room.

Soon, the content of Taylor's formula derivation was completed, which took up only half a page in total.

Finally, he drew a coordinate system, took the origin as the endpoint, made a ray at an angle of 45 degrees, and wrote down the final formula.

【tan(π/4)=1】

【π/4 = 1 - 1/3 + 1/5 - 1/7 ++(-1)^k (1 /(2k+1))+】

"how?"

Hong Fan threw down the charcoal pen, thinking about the solid foundation of his university, he couldn't help but feel at a loss when he drew his sword and looked around.

But he didn't get the expected admiration.

"Mr. Fan, what do you write on these ghostly symbols?"

Wen Zhongguan suppressed his temper and asked.

Hong Fan immediately realized that the symbol systems of the two worlds were not connected at all!

Not to mention various symbols and English letters, even numbers are written in completely different ways.

So, he embarrassingly let go of his superior demeanor, and compared all the symbols and concepts in the entire deduction system with Wenzhongguan one by one.

After more than half an hour of detailed communication, Hong Fan realized that the "professional title" of Wen Zhongguan's master craftsman and the "theoretical research" of the instrument maker supervisor were not in vain.

Concepts such as coordinate systems, trigonometric functions, functions, derivatives, calculus, etc., the latter are already understood.

At the same time, both Wen Zhongguan and Qian Hong also knew that this young gentleman was not completely talking nonsense, and he really had some accomplishments in numerology.

After the communication was over, Hong Fan rewritten the above derivation process using the symbol system of the monitor.

This time, when he put down the charcoal pen, except Zhu Jia and the two second-time craftsmen who were still in a daze, the master craftsman and the master craftsman had their eyes glued to the paper, so they didn't care about anything else.

As time passed, the more the two middle-aged people watched, the more they understood; the more they understood, the more shocked they were!

In Hong Fan's previous life, the Taylor formula was the result of the early eighteenth century.

This set of tools can approximate complex functions as simple polynomial functions, and convert nonlinear problems into linear problems.

In addition, it can also be used in finding limits, judging the extreme value of functions, finding the value of higher-order derivatives at a certain point, judging the convergence of generalized integrals, approximate calculations, and proofs of inequalities, etc.

Finding a π is just one of the applications.

When the Taylor formula appeared, Newton was still alive, and Taylor was one of the most important representatives of the Newtonian school.

Of course, by the time Hong Fan was in college, this was already an "ancient" thing, and it belonged to something that any mathematics undergraduate should understand as soon as he enters the university.

But in Dahua, this is the frontier and cutting-edge of seriousness!
PS: Speaking of which, although the author’s master’s degree is in finance, his undergraduate degree is from a serious mathematics department. From elementary school to high school, he has held mathematics and physics competitions and won some national awards.

But now that I am over thirty, all of the above have been scattered; even if I pick up the book and read it again, I can't even find the feeling of deja vu.

Therefore, if there is anything wrong with the theoretical stuff, everyone will just laugh it off; after all, Hong Fan's knowledge level in setting is much higher than that of me as the author.

In addition, the recommendation ticket for the new book issue seems to be very important, please pass by and vote for the recommendation ticket, thank you~~~
(End of this chapter)