Greetings, Mister Principal

In just one hour, Reiner unified the four most common special curves in the low-level magic spell model into a mathematical formula. For Reiner, this was the basic high school mathematics knowledge. He didn't spend much time deriving it, but Claire and Dana were still stunned by the process.

Especially Dana. In the past, she always thought that mathematics was a useless and very difficult subject, but at the moment, in Reiner's mathematics, there was a certain fascinating charm.

And Claire could only keep the confused expression. . .

"Mr. Principal, since these four curves can be unified into this function equation, can other curves also be expressed in this way? For example, the Demira spiral that constructs the spell Surge?"

Dana asked, she felt that she had never been as curious about mathematics as she was now.

Surge was a low-level spell that would create vortexes in water currents. Although in the hands of high-level mages, this spell could create vortices that would swallow ships, in the hands of apprentices, the biggest use of surge was to wash clothes and dishes.

As a work-study student, Dana was probably most familiar with this spell.

"It's possible, but I think you need to derive it yourself."

Reiner didn't give her answer directly. He had seen the light of seeking knowledge in Dana's eyes. For a student, interest was the best teacher. Now, he had successfully aroused Dana's heart of inquiry, the rest was to give her proper guidance.

"So this is what you call an improved spell model?"

Claire realized what Reiner said, indeed, although, from an external point of view, different functional equations did depict the same trajectory, their essence was already very different.

Although the spell model had not changed in any way, it had indeed been "improved".

This was a purely mathematical derivation, a process of logical thinking, without mobilizing any magic, without casting any spells.

If such a thing could be done, then was there a way to deduct magic by relying solely on mathematical proof and deduction?

Claire began to think about the true role of mathematics. Luna Nova Magical Academy did not have a special mathematics class. The students were only exposed to mathematics in courses involving spell models, such as the magic circles and magic formations. Even Claire did not really delve into mathematics beyond constructing spell models.

"Let me give you some homework. Please represent the magic model of the Illumination spell in polar coordinates. We will check the results in the school square three days later. Of course, you will still need to complete the math test as well."

Looking at the two girls who were thinking about it, Reiner said, making Dana's expression slightly stiff, and she nodded bitterly.

"Okay."

"Your birthday is coming. If you do well, for example, if you successfully cast an illumination spell, I will consider making a big cake for you to celebrate it."

Reiner said again. It immediately made this thrifty girl's face lit up.

"Really?" "How big is the cake?"

Of course, at the same time, Claire's eyes were also shining, and her eager look was like a cat with paws outstretched, watching the food in front of her and ready to go.

"You will know then."

Reiner was a little helpless. Girls were born with no resistance to sweets, especially girls in adolescence, who often had a hard time deciding whether to get more calories and maintain their figures, but it seemed that Claire didn't care at all.

"Now."

Reiner checked the time.

"I have to sort out today's gain."

......

Research about a new coordinate system and the functional equations of ellipse, hyperbola, parabola, and other curves in this coordinate system.

Reiner read the paper again after finishing writing.

This paper was very simple. It was almost a revision of what he had explained to Dana in the classroom this afternoon. In addition to the elliptic hyperbola and parabola, Reiner also derived the polar coordinate equations for other curves such as the Demira spiral, and incorporated most of the curves that appeared in low-level spells into the polar coordinate system.

Of course, just like when Thales Anakshi proposed the Anakshi theorem of triangles, the world's feedback did not appear, and Reiner's heart lake did not have the slightest ripple.

Sighing softly, but Reiner didn't feel too much regret, at least he could still use these theories when he advanced.

Generally speaking, the criterion for judging where an apprentice had advanced to the first-ring mage was whether at least one first-ring spell could be engraved into the apprentice's soul.

This statement was a bit difficult to understand. Reiner summarized it roughly after reading the relevant literature.

If a mage was a computer, then Heart Lake was equivalent to the operating system, and engraving a circle of a spell into the soul was similar to installing a program software in the operating system.

The spell engraved into the soul would cause a certain degree of change in the heart lake. At the same time, the casting process of this spell would become very simple, so fast as to open an application on a computer.

Other spells still needed to be re-constructed, which was relatively cumbersome. At the same time, the spells that a person's heart could hold were limited and could not be inscribed infinitely, so choosing the spells to inscribe was also very important.

Reiner also learned the biggest difference between ancient magic and modern magic, that was the way of construction.

Using a computer as an example again. The ancient mage was equivalent to a computer without any application software. All magic needed to be programmed in real time, and once it was cast, it must be programmed repeatedly. This shortcoming was obvious. It was that the requirements for the mage were very high, and the difference between every mage was big. The advantage was that it could adapt to changes and was quite flexible.

The modern magic pioneered by Hermann Braggs was to fix each spell and build a model of the spell. A mage only needed to inject magic into it to use the magic, which was like encapsulating the program into software, when needed, they just needed to activate it.

As a result, magic could be popularized. Although it had become somewhat inflexible, it was more approachable.

One of the spells that Reiner chose was a simple fireball. This spell had a certain amount of lethality enough to protect himself. At the same time, Reiner's research on the combustion reaction could also help improve this spell.

Most importantly, Reiner had always wanted to experience the thrill of casting a big fireball with his hands!

At this time, he was sitting in his room. On the desktop was the spell model of fireball. It had thirty-two spell nodes and a hundred and three magic channels, including straight lines, perfect circles, parabola, and hyperbola. Although the entire model was asymmetrically distributed, it also had a strange aesthetic.

Getting ready, Reiner glanced at the spell model again, then slowly closed his eyes, and began to build the fireball spell model