Chapter 220

When Lena opened the paper, he saw silis's handwriting.

Correct and meticulous, at least we can see that the author of this paper is very serious about the paper.

The content of the paper is just like the title, which is to explore whether various forms of motion can be integrated into one equation. At the beginning of the paper, he listed all the known forms of motion equations and some previous contents that have been integrated.

For example, linear motion, whether it is uniform linear motion or variable speed linear motion, can be explained by an equation, but this equation is not applicable when it comes to curve motion.

Based on this, the paper starts to study whether the curvilinear motion can be integrated.

Cyris first worked out the equation of motion on a concave surface, and then worked out the equation of motion on a convex surface, and integrated it into a similar form. He found that the two equations could be changed into the same form, and when one of the eigenvalues was zero, the equation became the equation of linear motion!

This may seem like an amazing discovery, but there are also problems.

There is only one sign difference between the two surface equations, one of which is a positive sign and the other is a negative sign. In fact, this is a very good explanation. After all, the two motions seem to be opposite mirror motions.

But the minus sign is in the open root.

This means that in order for a formula to hold, it is necessary to root a negative number, which is unprecedented in mathematical rules.

Even an ordinary magic apprentice can say that there is no way to square root a negative number. This formula is obviously wrong.

Many mages in the past may have deduced this step. Seeing that there was a mathematical irrationality, they stopped their exploration and thought that the unification of kinematic equations could not be achieved.

But his stubborn head didn't give up. He thought hard and put forward a concept in order to continue to perform.

Since negative number can't open square root, then design a number, its square is negative!

Cyris defined a number I, I ^ 2 = - 1, that is, the square of I is - 1, and the square root of - 1 is I.

He called the number imaginary, corresponding to the actual number, which is a hypothetical number.

After getting the concept of imaginary number, cyris's next derivation is flowing. He integrates curve equation and linear equation, as well as circular motion and simple harmonic vibration. In the process of derivation, cyris finds that trigonometric function can be transformed into exponential form by imaginary number in a sense.

Cyris spent a lot of time, exhausted all means, and finally got a formula.

Lena turned the page, and after a lot of proof on the previous page, the content on this page was extremely concise.

There is only one formula.

e^πi+1=0。

This formula includes engineering base, PI, 1 and 0, plus sign and equal sign, and imaginary number I.

It seems so simple and elegant, as if the whole mathematics is contained in it.

Lena knows that this formula is called Euler's formula on earth, also known as God's formula, which can be said to be one of the most important formulas in the field of mathematics.

But there is no doubt that the concept of imaginary number has a great impact on normal people.

One apple and two apples, people can clearly realize that this is a natural number, and the negative number derived from it is also easy to understand. As for irrational number, it can also be accurately expressed on the coordinate axis.

But imaginary numbers are different.

No one can say what I is or how to express it. People can't understand the meaning of this number.

It's as if the numbers were simply created to explain cyris's formulas.

It's hard for the world's mages to understand.

Lena already knows why the vice president of Bordeaux thinks that cyris's thesis is "meaningless", because even if there is no imaginary number, the magic model can be constructed smoothly, at most it is just a little troublesome. If imaginary number is introduced, many things that were agreed in the past need to be changed, and the extra theory about imaginary number It has no impact on the real world at all.

Because the imaginary number itself is a system that can exist independently.

With a sigh, Lena turned the page.

After establishing the whole system of imaginary numbers, cyris continued to explore. When he studied simple harmonic vibration, he found that any periodic motion can be regarded as the superposition of sine waves with different amplitudes and phases, just like different keys on a piano, which can be combined into different chords.

Through calculation, he established a set of mathematical method to decompose the periodic motion into the result of adding countless sine waves. In order to explain this method, cyris used a lot of discussion to explain it. This method he named it cyris transformation, which can transform the continuous periodic function in time into discrete function in frequency domain, and expand the series under a certain eigenvalue It is called the cyris series.In this discussion, cyris has tried his best to explore the application of imaginary numbers in the real world, but he has achieved nothing except this mathematical transformation method.

Reiner knows that although imaginary numbers are extremely important, they are far ahead of the times in today's world of mathematical level. Even the simplest equations describing electromagnetic fields that can apply imaginary numbers were only proposed this year. At that time, ten years ago, there was no theory that could make imaginary numbers useful.

Not to mention the group theory, probability theory, series expansion, function of complex variable, wave equation, quantum mechanics and so on, which have not yet formed a system in mathematics, how important the imaginary number plays in the microscopic research.

As for the cyris transformation, it may be in the far future. When the mages thoroughly study the electromagnetic wave, they will be able to apply it. At that time, some people will be surprised at this epoch-making theory.

Cyrus oldman's research is beyond the times, but the evaluation is "meaningless".

What an irony.

At the end of the paper, cyris repeatedly emphasizes the correctness of his proof. At the same time, he thinks that although these theories may not seem to have any effect now, perhaps in the future, new discoveries will prove their value.

Even until the end, this formula and the theory behind it have not found any value, cyris wrote. The exploration of mathematics itself is its significance.

Lena put down the paper, his heart mixed feelings, at this time, mother Hedwig's hand slowly took Lena's hand.

"Mother Hedwig, your son's paper is correct."

But for an old man who didn't even know a word and kept it for his son's sake, this paper, and the ideas contained in it, might not have appeared for many years in the evening.

Mother Hedwig was stunned for a long time when she heard Lena's words, as if she wanted to say a lot and couldn't say a word. She tossed and turned a thousand words in her heart and finally turned them into a short response.

"I knew you were right, Cyrus."

As the sun sets, the afterglow of the setting sun shines through the open window on mother Hedwig's side face, leaving a golden color.

Bright and dazzling.

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