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

Dana, in particular, used to think that mathematics was a useless and very difficult subject, but now, in Reiner's writing, mathematics has a certain fascinating charm.

Claire, on the other hand, can only keep "meow meow??? The expression of the expression.

"Mr. Chancellor, since these four curves can be unified into this functional equation, can the other curves also be represented in this way? For example, the Demira spiral that constructs the tidal surge? ”

Dana asked, feeling like she had never been as curious about math as she was now.

Tidal surge is a low-level spell that creates whirlpools in the flow of water, and while in the hands of high-level mages, this spell can create whirlpools that devour ships, but in the hands of mage apprentices, the greatest use of tidal surges is for washing clothes and utensils.

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

"Possibly, but I think you'll have to figure it out yourself."

Reiner left a suspense, he had seen the light of curiosity in Dana's eyes, interest is the best teacher for a student, and now that he had succeeded in arousing Dana's inquiring heart, the rest was to give proper guidance.

"So that's what you call a modified spell model?"

Claire realized what Reiner had said, and that, although it was true that different functional equations did depict the same trajectory from the outside, they were very different in nature.

The spell model has not changed in any way, but it has indeed been "improved" in the world on paper.

This is a purely mathematical derivation, a process of logical thinking, without any magic or spell, to complete this unity.

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

Claire began to reflect on the true role of mathematics, Crescent Academy did not have a special mathematics class, and students were only exposed to mathematics in courses involving spell models such as magic circle science, and even Claire did not delve into mathematics except for building spell models.

"I'll give you an assignment, that is, to embody the magic model of the illumination technique in polar coordinates, and after three days, we will test the results in the school square, and of course, we can't put down the math test papers in the past few days."

Looking at the two girls who were lost in thought, Reiner said, causing Dana's expression to pause slightly, and she could only nod bitterly.

"Okay."

"Your birthday is coming soon, and if you're doing well, like successfully performing a light spell, I might consider making you a big cake to celebrate."

Reiner said again, and the eyes of the usually thrifty girl immediately brightened.

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

Of course, Claire's eyes also lit up, and her eager appearance was like a kitten with its claws outstretched, looking at the food in front of her.

"We'll find out then."

Reiner is a little helpless, girls are naturally not resistant to sweets, especially adolescent girls, often have to fall into the entanglement of sugar intake and maintain figure, but it seems that Claire doesn't care at all.

"Now."

Reiner looked at the time.

"I've got to sort out what I learned today."

......

"A new coordinate system and its ellipse, hyperbola, parabola and other curves under this coordinate system function equation study".

Reiner finished writing his paper and flipped through it again.

In addition to elliptical hyperbolas and parabolas, Reiner also deduced the polar equations for other curves such as the Demira spiral, and incorporated most of the curves that appeared in the low-order spells into the polar coordinate system.

Of course, just like Thales back then. Anakhy came up with the anakhy theorem for triangles, but the world's feedback did not appear, and Reiner's heart lake did not ripple in the slightest.

He sighed softly, but Reiner didn't feel too sorry, at least he could use the theories when he advanced himself.

According to common sense, the criterion for judging an apprentice's advancement to a one-ring mage is whether or not he can engrave at least one one-ring spell into his soul.

This statement is somewhat difficult to understand, and Reiner summarized it roughly after reading the relevant literature.

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

Spells engraved into the soul will cause the heart lake to change to a certain extent, and the process of casting this spell will become incredibly simple, as fast as clicking on an app on a computer.

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

Reiner also learns the biggest difference between ancient magic and modern magic, and that is the way it is constructed.

Or take the computer as an example, the ancient mage is equivalent to getting a computer without any application software, all magic needs to be programmed instantly, and once cast, it has to be repeated programming to achieve, such a disadvantage is obvious, that is, the requirements for the mage himself are very high, individual differences are huge, and the advantage is that it can be improvised, quite flexible.

And Herman. The modern magic pioneered by Lord Braggs is to fix each spell and build a spell model, and only need to inject magic into it to use magic, which is like encapsulating a program into software, and clicking on it when needed.

In this way, magic was able to become more popular, albeit a little inflexible, but more approachable.

Reiner's chosen spell is a simple fireball, which has enough lethality to protect itself, and Reiner's research on the combustion reaction can also help improve the spell.

On top of that, Reiner has always wanted to experience the thrill of rubbing a big fireball by hand!

At this time, he was sitting in his room, and on the table was a spell model of the fireball spell, with thirty-two spell nodes and one hundred and three magic channels, including straight lines, perfect circles, parabolas and hyperbolas, although the whole model was not symmetrically distributed, but also had a certain strange beauty.

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