"Kid...... I don't know how to answer you, of course, not that it can't form a magic circle.

"But I'm not sure exactly what it can do, or rather, how ...... it This structure is a bit complicated......

"I think a lot that it should be able to participate in the construction, but this construction ......"

After a while, Curry gripped his beard with his hands, and the two thick eyebrows were almost twisted together.

His words were staccato and intermittent, as if he were thinking and organizing his language, trying to make the clearest explanation for Rogers:

"However, the structure with the nature of infinite circulation must greatly reduce the loss of mana, which is likely to increase the effectiveness of magic.

"When the mana can continue to circulate in the array without stress, it also means that there is no need to increase the insurance process of mana overflow, and at the same time, the threshold for use is greatly reduced......

"And most importantly, it's a symbol, a symbol that easily connects time and space...... I don't know how to express this kind of thing to you......"

At this point, Kuli seemed to have given up completely, and he no longer tried to explain anything, but just concluded:

"Anyway! This structure you came up with is great! It's so good that I don't know how to praise you! I still need to think and research more about it! Whatever the outcome, I'll definitely let you know!

"As for the credits, you still need to wait for me to discuss with the vice principal, after all, this contribution of yours will be great for the entire magic world!"

Currie propped up his heavy glasses with his hand, then slammed Rogers' chest with his huge fist, his tone full of admiration and admiration.

"Is it really possible?" Rogers heard Curly's explanation, and his face showed a rather interested look, he pondered for a moment, and then followed: "Professor, I actually have an advanced version of the structure hypothesis. ”

"Advanced?" Kuli was stunned, he didn't quite understand how this could be advanced.

"That's right, Professor." Rogers tossed the note aside and began to try to make a gesture with his own hands:

"Let's take the concept of a ring structure a step further, for example, as a closed surface, which looks like a ring, but the peculiarity is that the inside and outside are actually connected.

"When you look inside it, you can see that it also looks like a bottle. Passing through the bottle from the inside or outside, it is not possible to reach the other side of the bottle, but must be done by extending or bypassing the central axis......"

The Klein bottle is a mathematical object, and there is no actual three-dimensional entity that can truly take on its special shape.

Rogers had to painstakingly describe to Curley this purely mathematical concept, which existed only in the imagination, through a brief narrative and various metaphorical additions.

"It is capable of tending to symbolic concepts such as infinity, continuity, and self-referentiality, and can be called the Endless Bottle ......"

Currie was at first at a loss, having some difficulty understanding the abstract concepts that Rogers was talking about, but as he continued to compare and argue, his expression gradually became serious.

But as time passed, a lot of shock and sluggishness slowly appeared on his rough face, and he didn't know whether he understood it or not.

"Professor, do you think it's possible for this structure to be realized in magic? Can it be used to construct magic circles? ”

Rogers saw that something didn't seem right with the other party, and asked tentatively.

"Huh? Oh...... Should...... Is that okay? ”

Kuli's face showed a frozen expression at the moment, and his eyes were fixed in the direction of a void, as if he had completely lost his perception of the world around him, and was only responding instinctively.

"Is this okay?" Rogers pinched his chin, thought for a moment, and gestured with his hand in the air again:

"Professor, you should be very clear about the concept of the cube, which is the three-dimensional generalization of the plane square, so what if we try to generalize the cube again? In addition to the length, width, and height, add a line pointing in the fourth direction......"

Rogers is describing a hypercube at this moment, and its basic concept is much easier to understand than the Klein bottle.

It's just that this abstract geometric structure is not limited to the imaginary four-dimensional space, but can also be generalized to higher dimensions, just as the cube can be generalized to the hypercube.

Because of this, it gradually becomes more complex and abstract.

Kuli's pupils slowly dilated, his originally sluggish expression slowly became alert, his brows furrowed even tighter, and fine beads of sweat appeared on his forehead.

He trembled and grabbed Rogess's hands that were scribbling in the air, the muscles on his face began to twist inexplicably, and his lips trembled and he growled:

"Don't say any more!"

The roar seemed to come from deep underground, and in an instant it reverberated throughout the classroom.

The bodies of all the students were stiffened at this moment, as if they were facing the shock of a predator from a higher rank, constantly oppressing their hearts and imprisoning their bodies.

"I'm sorry, I didn't mean to, but you can't go on! Got it? ”

Currie let go of Rogeth's hands and warned softly and gravely.

"I know, everything is up to the professor." Rutgers adjusted to the soothing body from the stiffness and replied sincerely.

It was because he deeply understood Kuli's character and knew Kuli's impression of himself that he dared to confide this knowledge at will.

And judging from the other party's reaction, it seems that the benefits this time are much higher than the last conversation with Yalana.

"You first follow me to the teaching alchemy platform, and watch the carving array skills I teach nearby, and when the lecture is finished today, I will have a good talk with you."

Satisfied with Rogers' obedience, Curry asks him to follow him to his teaching desk.

Rogers made eye contact with Alina, and quickly caught up with Professor Curly.

A little impatience rose in his heart, and he was even speculating about how much that knowledge could bring to the growth of his strength.

After all, in addition to being burned on the physical object, the magic array can also participate in the release of spells, which is also one of the necessary conditions for constituting realm magic.

"Rutgers is going to be fine, right? Was Professor Curly angry just now? Rufia patted her chest and looked in the direction Rogers had left, and let out a voice of apprehension.

Several of the students around them had the same question in their minds, they didn't understand what Rogers was telling Professor Curly, but vaguely understood that it was about geometry.

But why did a simple intellectual conjecture provoke Professor Curly to react that way?

In anger, Rogers had a shallow suspicion and tried to teach Professor Curly as a mentor.

Even in the process of narrating, he vaguely satirized Professor Kuli's ignorance, which caused the professor's anger.

"But looking at the professor's appearance of favoring him so much, he should also value his talent, and it is estimated that at most a few reprimands, nothing will happen."

Alina turned to look at Rufia and explained in a reassuring tone.

Her volume was not small, and the people around her heard it very clearly, and then they all showed expressions of understanding.

It is worthy of Rogers, and only the little demon king of Hilmi Academy would dare to do such a bold deed.

The change in the demeanor of several people was reflected in Alina's eyes, which made her breathe a sigh of relief imperceptibly.

Then she gritted her teeth secretly, not understanding why she had to help Rogers clean up all this mess because of a look from him.

"Can I share an alchemy table with you?"

Alice approached Alina's side with a soft inquiry, her eyes bright and gentle, and her smile filled with just the right amount of friendliness.

"Because the students gathered at the alchemy platform where I am are are a little unconventional, I wanted to make a place for them, and I happened to see that there are only two people on your side......"

She met Alina's calm gaze and carefully explained her story.

"They just want to get close to the Holy Maiden to gather extra numbers, and after you leave, you can really solve this problem very well." Alina replied lukewarmly, without acceptance or rejection in her words.

Rufia observed Alina's reaction, and also put on a distant look, not taking the initiative to answer the saint's reply.

After getting along with Alina for a long time, she can clearly feel that Alina doesn't like the saint very much, and even has an inexplicable resistance.

"Thank you."

Alice thanked them and came to the two of them, and didn't say anything more, just quietly waiting for the practical lesson to begin.

After a while, a pair of fiery red hands composed of magic suddenly appeared in front of the three of them, and the carving knife was also pinched in their hands.

"When you open the fourth page of the textbook, I will burn the concentrating structure of a simple monolithic magic circle, and look at it carefully.

"When I burn, I will evenly inject magic into the carved lines, and once I burn successfully, I can also suck the magic array out of the stone slab.

"It won't last long, but you can still use it to amplify the power of ordinary spells."

Kuli's voice reached the ears of each student, and the magic hands demonstrated the delicate lines, as well as the various details and angles within them.

Every one of his knives was precise, without a hint of hesitation or error, and everything was as smooth as if the operation had become instinct.

When all the carvings are completed, the magic flows between the streamlined lines, and the entire magic circle takes on a dazzling brilliance.

"Do you want to start first?"

At the end of the demonstration phase, when the students were about to try their hand at carving, Alina glanced sideways at Alice and asked if she wanted to start first.

"Miss Alina, would you like to start first?"

Alice's lips outlined a pure, well-proportioned smile, and her tone was soothing and equally inquiring.

In the presence of St. Herthe's students, the saint is mostly gentle, and she expresses her opinion in a calm tone, both in speech and in response to others.

The rhythm of her words has always been so leisurely and calm, which makes people feel relieved and comfortable, and only once did the students of Hilmi Academy show their majesty when they abuse each other in the name of Rutgers.

But Alina is different from the average student, she has seen Alice dressed as a commoner girl in the bazaar.

At that time, Alice was worried, panicked, and even hugged Rogers and cried that night.

Therefore, for Alina, the saint in front of her is not so unattainable, and she feels that she will not be affected by the so-called saint's brilliance, and she is not in the mood to excuse each other.

"It doesn't matter who starts first, it won't be much different anyway."

Alina picked up her paintbrush and carefully traced the magic circle against the drawings in the book.

Ordinary students did not have Kuli to teach the art of one-knife forming, so they had to use the handwriting of the brush to assist in engraving.

"Really? That's what Miss Alina thought. Alice chuckled in agreement, watching as she watched the other man draw earnestly.

"It's not something to think about, it's just a fact that it's going to happen."

Alina's eyes were focused, her tone was steady, her fingers were nimble and skillful with her brushes, her wrists moving lightly and fluidly, each stroke precise and powerful, without hesitation.

"No one can decide what hasn't happened yet." Seeing that the other party was so resolute, Alice showed a slight emotion and helplessness on her face: "So, can you please wake up that child, I want to meet her." ”

"Ask Rogers, he caught him." Alina's response was crisp and neat, as if it had nothing to do with her, and when a line was perfectly closed, she slowly raised her eyes and looked straight at Alice, and said with obvious mockery:

"And the kid in your mouth is a cursed creature pointing at Rogers, and you almost killed him."