I’m Really Not Faye

After noticing that His Royal Highness "Quin" was attentive inside, Lynch suddenly didn't know what to say.

Even he can think of how much he will suffer in his heart when he cannot successfully become a mage at a certain time in the future!

Under the superposition of the former "halo" and the reality of "dreality", and the state of mind can remain calm, then he is Sage!

There is a saying in the world that is basically inseparable.

That is, apart from your parents, basically no one wants you to live better than them.

At that time, Lynch didn't say "getting down to the ground", just a group of strange gazes was enough to make his thoughts go to extremes.

Revenge has always been the same theme.

If Lynch couldn't beat the wind and waves for the rest of his life, that would be fine.

But in the future, he will only notice this turning point when he is given up and transferred to the "Secret Hall of Qi Ling".

At that time, he was the devil mastering power!

The mountains and rivers change color, the sun and the moon are filthy and dark.

Lynch suspected that he had just crossed the route of a "doomsday lord".

He couldn't help clenching his fists, and in accordance with the arrangement of that Queen Quinn, he wished he would embark on a crazy road.

Even if you don't have a disease, you have to get out of it.

Lin Qi silently lowered his head and re-examined the mysterious shadow behind him. The manifestation of Qi Ling symbolized "chaotic darkness."

"The above is my reasoning." He summed it up.

"Very well, you have reached the point of nuanced observation from the outside."

Qi Ling faintly replied behind him, with a hoarse and ethereal voice.

"The problem of externally observing the world is over, and the rest is for internal discussion."

"Please crush the meaning of my emblem in another dimension."

The constantly transfiguration Qi Ling said to Lynch's instructions.

At this moment, the black clouds outside the window are pressing down on the city, as if a squally storm is about to come.

Lynch breathed silently.

Crushed?

The mark on the emblem is the method of cutting a circle.

A way to find the pi ratio of 3.1415926.......

Lin Qi's eyes narrowed slightly, as if beginning to grasp the clues of the problem.

It's not Pi, and it certainly has nothing to do with Pi.

Since the entire emblem of Qi Ling is the method of cutting the circle, it is ultimately impossible to escape the milestone in the process of obtaining the pi.

Lynch calmed down slowly, and carefully recalled the era that was ended by that man, Sir Isaac Newton, after the circle-cutting method developed to its extreme.

When Newton proposed this method, no one in this world took the road of dividing polygons.

Lynch took a deep breath, and his thoughts returned to the era of 1666.

Because of the outbreak of the Black Death, Newton had to be isolated at home. At this time, he became interested in some simple calculations.

Such as (1+x)^2=1+2x+x^2.

(1+x)^3=1+3x+3x^2+x^3

(1+x)^4=1+4x+6x^2+4x^3+x^4

Generally to this scale, it is the ceiling for the thinking of top mathematics students of average junior high school students.

Calculating this way is actually re-applying (1+x) to the latest calculation, adding one more power, and so on.

However, Sir Newton found a shortcut.

You can get the answer directly without doing complicated calculations.

He saw these coefficients before the x power, and he was completely aware of a familiar fact.

1

1, 1

1, 2, 1 (2 power)

1, 3, 3, 1 (3rd power)

1, 4, 6, 4, 1 (4th power)

...

All the way down to the x-th power is this well-known triangle sequence (Pascal's triangle, Yang Hui's triangle) both in China and the West.

Lynch clenched his fists slowly, and this triangle was a good calculation compared to continuously looping over the new formula one more time (1+x).

Because the addition of two adjacent bits is the new value under the triangle.

Therefore, civilizations such as China, ancient Greece, India, and Persia have all discovered this law!

Relying on this triangle, the 20th power expansion sequence, he can also easily write it.

When Lynch once looked up the manuscripts of these ancient documents, even if he didn't understand the language, he could still see the same mathematical meaning from them.

This is the charm of mathematics!

Beyond language, across time, across culture, many mountains, igniting the fire of hope.

Even if the civilization falls in the torrent of time, the alien civilization that revisited sees the corresponding triangle, it can still understand the other side that human beings have reached.

Little by little, Lynch reviewed the whole idea of ​​calculating the π value, lest he would be interrupted, and he even felt that Qi Ling's momentum behind him was constantly soaring!

Immediately afterwards, Lin Qi silently wrote the next general formula for Yang Hui's triangle——

(1+x)^n=1+nx+n(n-1)x^22! +n(n-1)(n-2)x^33!+……

Binomial theorem!

By substituting the value of n at will, you can find the value of Yang Hui's triangle in the nth row.

There was a smile at the corner of Lynch's mouth. Mathematicians at the time knew this formula, but didn't know how to use it.

It looks beautiful, but just like Faraday and others discovered electromagnetic induction, Franklin attracted thunder and lightning, Ampere discovered electric current, and so on, they were all in contact with the giant "electricity" at the beginning, and they didn't know the actual meaning.

Knowing the presence of electric motors and generators is where they are really used.

Similarly, Newton also swiped his pen to overthrow the entire binomial formula and rebuild it!

He tried to ignore the original company's requirement that n must be a positive integer and directly substitute n=-1!

So the formula becomes (1+x)^-1=1-1x+1x^2-1X^3……

The finite Yanghui triangle began to move towards an infinite series.

Because in the original number of terms, you can rely on (n-n)=0 to make all subsequent terms 0.

But when n=-1, the originally limited number of Yang Hui's triangle terms will no longer be all zero, and the infinite series is infinite possibilities.

With this formula, Newton found that multiplying both sides by (1+x) at the same time will become 1=1, so it is indeed meaningful from a certain perspective.

Later, Newton tried to substitute n=12 into it, and it was also possible to expand polynomials.

At this point, the former Lynch began to shock, because the 12th power is the root sign!

You must know that the equation of a circle is x^2+y^2=1.

Therefore y=(1-x^2)^12.

This can be expanded into a new polynomial, just replace the polynomial x with -x^2.

(1-x^2)^12=1-12x^2-18x^4--116x^6……

At this point, the magical fireworks finally began to release!

Integrating both sides of the formula at the same time is the area, and the interval is between 0 and 1.

Take the left side (1-x^2)^12 and the result is a quarter circle——

π4!

The formula on the right, after integration is 1-16-140-1112-51152......

That is, π=4 (1-16-140-1112-51152...)

No one can believe that the infinite series on the right can actually calculate π!

Can be accurate to any digit after the decimal point.

Since then, the calculation of π has moved to another dimension. No one cuts the circle anymore, but continues to optimize this formula.

Such as integrating the 0-12 interval to speed up the convergence speed.

This is where Lynch's formula for calculating π scribbled in the second level of the path of the mage comes from.

Under the new integration interval, even only 5 items can be accurately calculated to 3.14161, with an error of two out of 100,000.

And to reach the 35-bit precision calculated by Rudolph with four quadrillion polygons, only 50 terms are needed.

Compressed years of work to one day!

After reading the origin of modern π numerical calculations, Lynch once fully understood the true meaning of that sentence——

Science is the primary productive force.

The most intuitive method is not necessarily the best method.

In contrast, studying the law can sometimes reach the other side faster!

Therefore, Lin Qi silently wrote the entire binomial formula inside the emblem, and then substituting 12 step by step, and finally got the simplest infinite series!

In an instant, Qi Ling's traditional circular cutting method was instantly misfired when faced with the epoch-making tool of "infinite series".

I was overwhelmed by Lynch as to the bottom of the valley!

The Spirit Power of possessing an absolute rational personality began to appear in the depths of Lynch's mind.

It's just that he has lost his dominant position, can only observe Lynch's behavior quietly, and can no longer resist.

Gradually, Lynch felt the power of the entire contract, slowly spreading throughout his body, and he began to have an inseparable relationship with that absolutely rational personality.

The other party's spirit and his spirit, as if ink is mixed with water, completely merged into one.

And the sign of this Qi Ling is that his eyes gradually become cold, without the slightest vitality.

Existence defines reality.

Nothing exists, and nothingness does not exist.

Therefore, if Qi Ling does not exist, the above simple argument cannot be refuted.

At this moment, he finally understood why these forces, which transcended all limitations, attracted many sages who were interested in contract magic in the philosophical sense.

Someone confided in Lynch's ear that Qi Ling is a myth in general meaning, not a real existence, but rooted in the hearts of all beings.

Someone also confided in Lynch's ear that Qi Ling was a spirit in the true sense, and was abandoned to a plane that could not be touched by any magic due to the agreement of the gods.

But no matter what the truth is, Qi Ling is eager to participate in reality.

Even if it's just borrowing the eyes of creatures to peer into the world.

Lynch felt the lingering power of the "absolutely rational personality" in his body!

He finally succeeded in surrendering this power to his own hands.

The spring of microprocessors has officially arrived.

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