Greetings, Mister Principal: The trajectory of the stars

In a corner of the Rainbow Tower, there is a lonely tower.

This tall tower located in the lush forest is not a straight structure, but spirals up. It is full of weird atmosphere, but it also exudes a wonderful sense of beauty.

This is the mage organization of the astrology system, the headquarters of the stargazers.

In an office in a high tower, a middle-aged man was deep in thought.

His fingers kept tapping on the table, as if he was considering a difficult question. The man's brows were furrowed, and he held a beautiful quill in his hand, but he still couldn't write any words.

Dong dong dong——

While the man maintained this posture, a rapid knock on the door interrupted his meditation.

He raised his eyebrows slightly, but soon sighed helplessly and put the quill back into the ink bottle.

"Come in."

After receiving a response from the man, the person who knocked on the door pushed open the door. It was a young man wearing the popular mage robe of the Rainbow Tower, with five golden edges flashing on the cuffs.

"Fenrir, what's the matter?"

The man asked. His student had never been very calm, and now he looked even more anxious.

"Teacher, I received an academic paper here."

The student known as Fenrir said respectfully and put the copy of the paper in his hand on the man's desk.

"Academic paper?"

At this time, the man remembered that his student was serving as a review member of the thesis review committee, which he had instructed in order to make this reckless student more mature.

But Fenrir should have received papers from low-level mages. Why should he tell himself about this?

"Teacher Regens, this is a mathematical paper written by Rainer Ian Gray."

Fenrir added.

"Mathematics? Reiner Ian Gray?"

The man, high-level mage Wilder Regens, looked at the cover of the paper.

Linard Ingle's paper on the electrolysis of water has long been spread in the Tower of Rainbow. This young mage apprentice is quite favored by the mercury scale, but to Wilder, he is just an ordinary genius. That's all, he didn't pay too much attention.

Wilder has long felt that the theory of the four basic elements has serious loopholes, and it is only a matter of time before it is overturned. Reiner Ingle is just following the trend of history and picking up a fish that slipped through the net.

But now it seems that this Reiner Ingle actually studies mathematics?

But even so, it has nothing to do with me.

Wilder glanced at his student but did not open the paper.

"Teacher, this paper describes a new coordinate system. I think this may be helpful to your research."

Fenrir understood what the teacher meant and explained again.

He knew that his teacher was studying the movement patterns between stars, and already had certain observation data and conjectures, but it was difficult to prove mathematically, which led to ridicule from many people among stargazers. You know, in In the eyes of most astrology mages, whose mystical sect dominates, the movement trajectories of stars should be perfect circles rather than the weird ellipses that Wilder insists on.

In this case, Fenrir happened to get this paper. After reading it carefully, he hurried here, hoping to help the teacher.

"Coordinate system?"

Wilder didn't have much idea at first, but when he picked up the paper under the gaze of his students and saw the title, the calm high-level mage's eyes also lit up.

"Derivation of curve equation?"

You must know that Wilder is currently unable to establish a complete and concise way to prove his ideas. Regardless of the content of this paper, at least the research direction is indeed consistent with Wilder's theory.

It seems that his students are not without merit.

Glancing at Fenrir, Wilder opened the paper.

When the word polar coordinates was first proposed, Wilder read it very slowly. He picked up the pen and followed the paper's ideas on the paper to calculate. When he fully understood the connotation, he put down the pen and sighed softly.

"What, what happened?"

Fenrir originally thought that he could help the teacher, but looking at Wilder who was frowning at this moment, the stone in his heart became high again.

"I just lament that I have overlooked such a simple thing. The idea of ​​setting up this polar coordinate is not difficult, but it is very clever. Maybe when you are in a high position, it is easy to overlook some basic things."

Explaining, Wilder turned to the discussion about curve equations.

The derivation process here seemed very simple to Wilder, who had already understood polar coordinates. When he saw Reiner unifying several common curves into a functional equation, Wilder felt a buzzing in his brain. stand up.

Isn’t this the answer I’ve been dreaming of! ! !

He stood up abruptly, causing Fenrir next to him to take several steps back in fright. Then Wilder immediately sat down again, picked up the quill, and began to calculate continuously.

Wild has three conjectures about the movement of stars, and he is currently using polar coordinates to verify these conjectures.

The first guess... established!

This is the most basic conjecture. Wilder believes that the movement trajectory of the stars surrounding the sun is not a perfect circle as thought in the past, but an ellipse. At this time, various observation data are substituted in polar coordinates. Among them, the derivation result presented is exactly the polar coordinate equation of the ellipse!

The second guess... established! !

Based on the first conjecture~IndoMTL.com~ Wilder calculated that when the stars orbit the sun, the area swept by the line connecting the stars and the sun per unit time is equal, which means that the stars do not move at a uniform speed. !

The third guess... established! ! !

The third conjecture is to demonstrate the relationship between the time it takes for a star to orbit a star and the semi-axis of its orbit. When the first two conjectures are true, this conjecture can be easily proven!

Three conjectures that have troubled Wilder for a long time have been mathematically proven. From this moment on, these three conjectures are no longer just conjectures, but laws!

Regens’ three laws about the movement of stars!

Buzz——

Wilder felt that the lake in his heart was turbulent like never before. Above the rising waves of the lake, stars were moving in strange trajectories. They were not perfect circles, but ovals of different shapes. !

This is the world’s feedback!

Closing his eyes, after a long time, Wilder slowly opened his eyes, feeling the majestic power in his body. There is no doubt that he has received enough feedback through the establishment of these three laws. As long as With a little preparation, you can successfully advance to the ninth level, and you are only one step away from being a legendary mage.

Wilder looked at the paper again and couldn't help but sigh again.

"Teacher, do you have any questions?"

Fenrir, who was afraid to speak, had previously sensed the resonance of magic in the room, and vaguely knew that his teacher should have received feedback from the world, but he did not understand why he still sighed.

"I am just feeling that the person who can write such a paper, if he is among us stargazers, he will definitely become the most shining new star. Unfortunately, he was snatched away by the mercury scale long ago. ."

Shaking his head, Wilder said helplessly.