In just one hour, Reiner unified the four most common special curves in the low-level magic spell model into one mathematical formula. For Reiner, this is the basic high school mathematical knowledge. He didn't remember it very clearly. He didn't take much time to deduce it himself, but the process still made Claire and Dana stunned.

Especially Dana, in the past, she always thought that mathematics was a useless and very difficult subject, but at this moment, in Reiner's writing, mathematics has some fascinating charm.

And Claire can only maintain the expression of "Meow Meow Meow Meow Meow Meow???"

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

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

The Tide and Surgery is a low-level spell that creates vortexes in the water flow. Although in the hands of high-level mages, this spell can create vortexes that devour ships, in the hands of mage apprentices, the biggest use of the Tide and Surgery is to clean clothes and tableware.

As a part-time student, Dana is probably the most familiar with this spell.

"It's possible, but I think it needs to be derived by yourself."

Reiner left a suspense. He had already seen the light of seeking knowledge in Dana's eyes. For a student, interest is the best teacher. Now, he has successfully aroused Dana's desire for exploration, and the rest is to give appropriate guidance.

"So is this what you call a modified spell model?"

Claire realized that what Reiner said was indeed, although from an external perspective, different functional equations do depict the same trajectory, but their essence is already very different.

Although the spell model has not changed at all, it has indeed been "improved" in the world on paper.

This is a purely mathematical deduction, a process of logical thinking. Without mobilizing any magic or casting any spells, this unity is accomplished.

So is there a way to deduce magic simply by relying on mathematical proof derivation?

Claire began to reflect on the real role of mathematics. Crescent Academy did not have special mathematics classes. Students came into contact with mathematics only in courses involving spell models, such as magic arrays. Even Claire did not study mathematics in depth except building spell models.

"I will assign you homework, which means to reflect the spell model of the light technique in polar coordinates. Three days later, we will check the results in the school square. Of course, we cannot put down the math test papers these days."

Looking at the two girls who were thinking, Reiner said, making Dana's expression slightly stagnant, and she could only nod her head bitterly.

"All right."

"Your birthday is coming soon. If you perform well, say, successfully casting the light spell, I can consider making a big cake for you to celebrate."

Reiner said again, making the eyes of the thrifty girl who was on weekdays brighten up.

"Really?" "What a cake?"

Of course, Claire was also emitting eyes. Her eagerness to try was like a kitten stretching out her claws, watching the food in front of her ready to go.

"I'll know then."

Reiner was a little helpless. Girls were born with no resistance to sweets, especially those in adolescence. They often had to get into the entanglement of sugar intake and maintaining their figure. However, Claire seemed to care at all.

"Now."

Reiner looked at the time.

"I have to sort out what I have gained today."

......

"Study on the functional equations of a brand new coordinate system and its ellipse, hyperbolic, parabolic and equal curves under this coordinate system."

After Ryner finished writing the paper, he read it again.

This paper is very simple. It almost records the content explained to Dana in the classroom this afternoon. In addition to the elliptical hyperbola and parabola, Reiner also deduces polar coordinate equations for other curves such as Demira spiral, and incorporates most of the curves that appear in low-order spells into the polar coordinate system.

Of course, just like when Thales Anakshi proposed the Anakshi's theorem for triangles, the feedback from the world did not appear, and there was no ripples in Reiner's heart lake.

He sighed softly, but Reiner didn't feel too regretful, at least he could still use these theories when he advanced.

According to common sense, the standard for judging an apprentice to advance to a first-ring mage is whether at least one first-ring spell can be engraved into the soul.

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

If the mage is a computer, then Xinhu is equivalent to an operating system, and inscribed a spell into the soul is similar to installing a program software in the operating system.

The spell engraved into the soul will cause a certain change in the Heart Lake. At the same time, the casting process of this spell will become extremely simple, quickly like clicking on an application on a computer.

Other spells still need to be constructed repeatedly, which is relatively complicated. At the same time, the spells that a person's heart lake can carry are also limited and cannot be engraved infinitely, so it is also very important to choose the engraved spell.

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

Take computers as an example. Ancient mages were equivalent to getting a computer without any application software. All magic requires real-time programming, and once cast, they have to be repeatedly programmed. This disadvantage is that they have very high requirements for the mage themselves, and they have huge individual differences. The advantage is that they can adapt to changes and are quite flexible.

The modern magic pioneered by Hermann Pragues is to fix all spells and build a spell model. You only need to inject magic into it to use magic. This is like encapsulating a program for software, clicking it when needed.

This is how magic can be popularized, although it has become a little inflexible, but it is more approachable.

One spell chosen by Reiner is a simple fireball technique. This spell has a certain lethality and is enough to protect itself. At the same time, Reiner's research on combustion reactions can also assist in improving this spell.

Most importantly, Reiner has always wanted to experience the pleasure of rubbing a big fireball with his hands!

At this time, he was sitting in his room, with the tabletop a spell model of Fireball, with 32 spell nodes and 103 magic channels, including straight lines, perfect circles, parabolas and hyperbolas. Although the entire model is asymmetrically distributed, it also has a certain strange beauty.
Chapter completed!