After noticing that His Royal Highness "Queen" 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 break through and become a mage smoothly at some point in the future!

　　 Under the superposition of the former "halo" and the reality of "dreadfulness", the mentality can still remain peaceful, then he is a saint!

　　 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 the stone", just a group of strange gazes were enough to make his thoughts go to extremes.

　　 Revenge has always been the same theme.

　　 If Lynch can't beat the wind and waves all his life, that's all.

　　It is possible for him in the future to discover this scene of turning around when he was 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 dark.

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

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

　　 Even if I don’t have a disease, I 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 "chaos and darkness."

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

　　 "Very good, you have reached the point where you are observing from the outside."

　　 Qi Ling faintly replied behind him, his voice hoarse and vague.

　　 "The problem of external observation of the world is over, and the rest is the problem of internal discussion."

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

　　 The constantly transfigured 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 coming.

　　 Lynch breathed silently.

　　 Crush?

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

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

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

　　 is not pi, so surely it has nothing to do with pi.

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

　　 Lynch slowly calmed down, 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, 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 up to this scale, it is the ceiling for the thinking of the average junior high school student in mathematics.

　　 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 (2nd power)

　　 1, 3, 3, 1 (3rd power)

　　 1, 4, 6, 4, 1 (4th power)

　　……

　　 all the way down to the x-th power, are the triangle series (Pascal triangle, Yang Hui triangle) that are quite famous both in China and the West.

　　 Lynch clenched his fists slowly. This triangle is considered to be a good calculation compared to continuously cycling the new formula one more time (1+x).

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

　　 So China, ancient Greece, India, Persia and other civilizations have discovered this law!

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

　　 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!

　　 transcends language, time, culture, mountains and mountains, igniting the fire of hope.

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

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

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

　　(1+x)^n=1+nx+n(n-1)x^2/2! +n(n-1)(n-2)x^3/3!+……

　　 Binomial Theorem!

　　 Substituting the value of n at will, you can find the value of Yanghui triangle in the nth row.

　　 Lynch smiled at the corner of his 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 that electric motors and generators appear, 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 Yang Hui triangle begins to move towards an infinite series.

　　 Because of the original number of items, it is possible to rely on (n-n)=0 to make all subsequent items 0.

When 　　 can be 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.

　　 And 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=1/2, and the polynomial can also be expanded.

　　 At this point, the former Lynch began to shock, because the 1/2 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)^1/2.

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

　　(1-x^2)^1/2=1-1/2x^2-1/8x^4--1/16x^6……

　　 At this point, the magical fireworks finally began to be released!

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

　　 to the left (1-x^2)^1/2 integration result is a quarter circle——

　　Π/4!

　　The formula on the right, after integration is 1-1/6-1/40-1/112-5/1152......

　　 is π=4 (1-1/6-1/40-1/112-5/1152……)

　　 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 0-1/2 interval to speed up the convergence speed.

　　 This is where Lynch's π calculation formula scribbled in the second level of the wizard's road is where it came 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.

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

　　 Compression of several years of work to one day!

　　 After reading the origin of modern π 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 shore faster!

　　 Therefore, Lin Qi silently wrote the entire binomial formula inside the emblem, and then substituted into 1/2 step by step, and finally got the simplest infinite series!

　　In an instant, Qi Ling's traditional cutting circle 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 spiritual power of an absolutely rational personality began to appear in Lynch’s mind.

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

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~lightnovelpub.net~ The other party’s spirit and his spirit, as if ink is mixed with water. , Fully integrated 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 a philosophical sense.

　　 Someone confided in Lynch’s ear that Qi Ling is a myth in general meaning, not real, 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. Due to the agreement of the gods, he was abandoned to a plane that no magic could touch.

　　 Regardless of the truth, 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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