In just one hour, Reiner unified the four most common special curves in the spell models of low-level magic into a mathematical formula. For Reiner, this was basic high school mathematics knowledge. He remembered I'm not sure, and I didn't spend much time deriving it myself, but Claire and Dana were still stunned for a moment during the process.
Especially Dana, in the past, she always thought that mathematics was a useless and very difficult subject, but now, under Reiner's writing, mathematics has a certain fascinating charm.
Claire, on the other hand, could only keep her "meow meow???" expression.
"Mr. Principal, since these four types of curves can be unified into this functional equation, can other curves also be expressed in this way? For example, the Demira Spiral that constructs the surge technique?"
Dana asked, feeling that she had never been more curious about mathematics than she was at this moment.
Tide is a low-level spell that creates whirlpools in water. Although in the hands of a high-level mage, this spell can create a whirlpool that swallows ships, in the hands of a mage apprentice, the greatest use of Tide is to clean clothes and tableware. .
As a work-study student, Dana is probably most familiar with this spell.
"It's possible, but I think you need to deduce it yourself."
Reiner was left in suspense. He had already seen the light of curiosity in Dana's eyes. For a student, interest is the best teacher. Now, he has successfully aroused Dana's heart of inquiry. , the rest is to provide appropriate guidance.
"So is this what you call an improved spell model?"
Only then did Claire realize what Reiner had said. Indeed, although from the outside, different functional equations did depict the same trajectory, their essences were quite different.
Although the spell model has not changed at all, in the world on paper, it has indeed been "improved".
This is a purely mathematical derivation, a process of logical thinking. This unification was achieved without mobilizing any magic power or casting any spells.
So is there a way to deduce magic that relies solely on mathematical proofs and derivation
Claire began to reflect on the true role of mathematics. Crescent College did not have a dedicated mathematics class. Students were only exposed to mathematics in courses involving spell models, such as magic circle studies. Even Claire did not go into depth other than constructing spell models. Studied mathematics.
"I will give you an assignment, which is to embody the illumination spell model in polar coordinates. Three days later, we will test the results in the school square. Of course, we can't put down the math papers these days."
Looking at the two girls who were lost in thought, Reiner said, making Dana's expression slightly stagnant and she could only nod bitterly.
"All right."
"Your birthday is just around the corner. If you behave well, for example, if you successfully cast the light spell, I can consider getting you a big cake to celebrate."
Reiner said again, making this usually thrifty girl's eyes immediately brighten.
"Really?" "How big is the cake?"
Of course, Claire’s eyes were shining at the same time. She looked eager to try like a kitten with its paws outstretched, looking at the food in front of her and getting ready to eat.
"We'll know when the time comes."
Reiner was a little helpless. Girls are naturally incapable of resisting sweets, especially those in adolescence. They often have to struggle between taking in sugar and staying in shape. However, it seems that Claire doesn't care at all.
"Now."
Reiner looked at the time.
"I have to sort out today's gains."
... ...
"Research on a brand-new coordinate system and its functional equations of ellipses, hyperbolas, parabolas and other curves in this coordinate system."
Reiner finished writing the paper and read it again.
This paper is very simple. It is almost recorded after revising what was explained to Dana in the classroom this afternoon. In addition to elliptical hyperbolas and parabolas, Reiner also made polar coordinates for other curves such as the Demira spiral. The derivation of equations brings most of the curves that appear in low-level spells into the polar coordinate system.
Of course, just like when Thales Anakshi proposed the Anakshi theorem of the triangle, the feedback from the world did not appear, and there was no ripple in Reiner's inner lake.
Reiner sighed softly, but he didn't feel too sorry. At least he could still use these theories when he advanced.
According to common sense, the criterion for judging an apprentice's advancement to a first-level mage is whether he can engrave at least one first-level spell into his soul.
This statement is somewhat difficult to understand. Reiner roughly summarized it after reading the relevant literature.
If the mage is a computer, then the heart lake is equivalent to the operating system, and engraving a spell into the soul is similar to installing a program software in the operating system.
The spell engraved into the soul will cause changes in the heart to a certain extent. At the same time, the process of casting this spell will become extremely simple, as fast as opening an application on the computer.
Other spells still need to be constructed repeatedly, which is relatively cumbersome. At the same time, there is a limit to the spells that a person's heart can carry, and it cannot be engraved infinitely, so it is also very important to choose the spells to be engraved.
Reiner also learned here that the biggest difference between ancient magic and modern magic is the way it is constructed.
Let's 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 in real time, and once it is cast, it must be programmed repeatedly. The shortcomings of this are obvious, and it is for the mage himself. The requirements are very high and individual differences are huge. The advantage is that it can adapt to changes and is quite flexible.
The modern magic pioneered by His Excellency Herman Braggs is to fix each spell and establish a spell model. You only need to inject magic into it to use magic. This is like encapsulating a program into software. When needed, Just click it.
From this, magic can be popularized, and although it becomes a little inflexible, it is more approachable.
The first-level spell that Reiner chose is a simple fireball. This spell has a certain lethality and is enough to protect himself. At the same time, Reiner's research on combustion reactions can also help improve this spell.
The most important thing is that 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. On the table was the fireball spell model. It had thirty-two spell nodes and one hundred and three magic channels, including straight lines, perfect circles, parabolas and hyperbolas. The entire model Although the distribution is not symmetrical, it still has a strange aesthetic feeling.
After making preparations, Reiner glanced at the spell model again, then slowly closed his eyes and began to construct the fireball spell model.