Did the villainous professor survive today?

Chapter 80 Klein's Magic Circle

"Can anyone tell me how to achieve lossless long-range spellcasting?"

Kroenke said, "Even simple ideas and guesses can be shared, and I will reward students with extra credits for their correct thinking."

Although Kroenke allowed people to speak and even offered the incentive of academic credits, the students below fell silent as they looked at the Möbius magic ring in Kroenke's palm.

There's no other reason than that I can't imagine it.

Allen squinted, staring intently at the Möbius magic ring in Krenk's palm.

Lossless long-range casting, Möbius strip —

He felt that the prototype of something amazing was gradually taking shape in his mind, but it was just one step away from completion.

Now he regretted sitting so far back, as he couldn't see the details of Krenk's spellcasting at all.

Maybe if we get a little closer, we can see it more clearly.

"Does nobody know?"

Kroenke asked again, "Even a guess is acceptable."

His response was still complete silence.

Perhaps because Allen had left such a deep impression on everyone in the previous class, some students subconsciously turned around and looked at the thin boy sitting in the corner of the classroom.

After all, it was he who brought out the Möbius Magic Ring last time.

Feeling the gazes of everyone, Allen could only shake his head, indicating that he had no other choice.

"Then, can anyone answer me, what are the characteristics of this magic ring?"

"The front is also the back." A student raised their hand.

"Hmm, anything else?" Krenk asked.

Another silence followed.

Kroenke added, "The beginning is also the end."

Upon hearing these words, a few faint arcs of electricity flashed through Allen's mind, and then, as if a light bulb had been lit, his eyes widened instantly and his mouth gaped open.

Agra instantly noticed Allen's change, and his pupils dilated as well.

You understand now?

"So you see, your thinking is still too limited, you haven't broken free from it."

Before Allen could figure it out, Kroenke drew a regular hexagon on the blackboard.

"As you can see, this is a regular hexagon with diagonals connected," Krenk paused, "but at the same time, it can also be a cube."

"The same image remains unchanged, but the way of thinking and perspective can jump from two-dimensional to three-dimensional."

"The only difference is the way you understand it."

"What does this mean?" Krenk asked himself, answering his own question. "Dimensions are never walls that can't be pushed open, but rather doors that can be opened at any time, switches that can be turned on and off, depending on how you perceive and understand them."

As he spoke, Krenk extended two fingers and gently pinched the Möbius magic ring.

"Your thinking has remained superficial from beginning to end; you've never considered that since a magic circle can transform from two-dimensional to three-dimensional..."

"Then—why can't it transform from three dimensions to four dimensions?"

Then, under the guidance of Krenk's right hand, the Möbius magic ring in front of him "grew" new curved surfaces from the ring and began to evolve towards higher dimensions.

The students held their breath, as if an invisible hand was pressing on their lungs at the same time.

This is a scene that is difficult to describe and extremely counterintuitive.

Afterwards, according to the students' recollections, some people said that Krenk's hand passed through the Möbius magic ring, but the flowing magic patterns on it were not disturbed at all.

Some people say that the magic ring is evolving in a strange direction, not up and down, not left and right, not front and back, but a fourth direction, a direction that has never existed in reality.

A very small number of people say that, for some reason, the magic circle that was originally on the surface suddenly appeared inside. No, to be precise, they are one, with no distinction between the surface and the interior.

In short, despite the various opinions, everyone ended up seeing the same final product.

The Möbius strip transformed into a bottle.

A bottle with no opening, no inside or outside, no beginning and no end.

Klein bottle.

"In this state, the starting point is the end point. Therefore, we can use this magic circle to create an invisible curved surface to connect two points in space that were not originally connected, thus achieving long-distance spellcasting without loss."

Kroenke said casually, "I've named it—the Klein Magic Circle."

The classroom was silent for a full ten seconds.

Then, dozens of students simultaneously gasped, amidst the sounds of chairs being pushed away, people instinctively stepping back, and the rustling of pages turning.

Unlike the previous three-dimensional magic circle, this Klein magic circle was more abstract and harder to understand, so many students turned their heads and looked at Allen for help, hoping that he could come out and explain something.

Stop looking at me!

Looking at the Klein magic circle in front of him, Allen felt like he was about to grow a brain.

Does anyone have any questions?

Kroenke straightened his tie.

Everyone looked at each other, their minds filled with countless questions, but they had no idea where to begin.

Under the impact of Klein's magic circle, the only thing they no longer doubted was why Klenk could become the chief professor at only 24 years old.

Krenk glanced at Mayon out of the corner of his eye and noticed that she was also stunned. The Klein magic circle in front of her was so shocking that she hadn't even reacted. Just how great was this magic circle?

[Your Klein magic circle has put Mayon into thought; the idea that you are a genius, not a fraud, is gradually refreshing her mind.]

[Points +3000!]

[Current points: 9000!]

"Teacher, is this our homework?"

A student asked a question, his voice trembling.

"Hehe," Krenk suddenly chuckled twice, "Let's figure out the three-dimensional magic circle first."

"The transition from two-dimensional to three-dimensional is a very easy concept to understand; it's simply a change from a two-dimensional plane to a three-dimensional structure."

"But the transition from three-dimensional to four-dimensional is an abstract concept, and it's difficult to understand through textbooks and hands-on practice alone."

Kroenke waved his hand gently, and the Klein magic circle seemed to tire, the flowing light on its surface gradually subsided, and it turned back into the Möbius magic ring.

"In another two weeks, the academy will organize an exam. I will commend the top five students in the exam, and the commendation will be that I will personally teach Klein the Magic Circle one-on-one."

There wasn't much reaction from the audience; everyone was still immersed in the long-vanished Klein magic circle, unable to pull themselves away for a long time.

Kroenke didn't give them time to process it. He glanced at the pocket watch in his pocket; it was about time.

"Alright, if there are no further questions, get out of class dismissed."

Krenk closed his pocket watch, stepped down from the podium, and called to Enya, who was staring blankly like the other students, "Let's go."

Enya remained unmoved, her mind focused entirely on the content of Krenk's lecture.

"Hey! Let's go!"

Kroenke raised his voice and patted Enya on the shoulder.

"Um?

Enya looked at Krenk as if waking from a dream, then nodded vigorously and followed behind him, leaving behind a group of students whose brains had shut down, sitting in their seats, letting their thoughts drift to the ends of the earth.

The only one that reacted was Meiwen.

Krenk's last words, "The top five will teach Klein the magic circle," reached her ears.

"Top five, huh?

Mei Wen murmured to herself.

Suddenly, as if struck by lightning, she clutched her head, utterly devastated: "I'm doomed, I've lost 15 points—"

"It's too late—"

This happened two weeks ago; even if death were reversed, it wouldn't take us back that long.

"Waaah~"

Meiwen let out a cute whimper.

As Kroenke walked out of the teaching building, the senior students who had been waiting for a long time became excited, but were then stopped by other teachers who were maintaining order to prevent them from affecting Kroenke's schedule.

Kroenke glanced at them briefly, then continued on his way.

Next, he was going to the principal's office.

But after Kroenke left, not a single new student was seen leaving the teaching building for a long time.

This left the many senior students who were waiting bewildered. What had happened?

Five minutes later, a freshman slowly walked out of the teaching building.

Upon seeing this, the older students immediately surrounded them.

"Hey! Student! What did Professor Krenk talk about today?"

"Is it still related to the three-dimensional magic circle?"

"Is it a new theory? Or is it an improvement on the three-dimensional magic circle?"

"Could I take a look at your notes, young man? I'll pay £1 for the rental fee."

"I'll offer £3!"

"I'll pay 5 pounds!"

"Hey! How can you engage in such malicious competition?!"

"That's called paying for knowledge! What do you know?!"

Hearing the commotion of the upperclassmen around him, the freshman did not react at all, like a walking corpse.

His mind was still replaying the bottle-shaped magic circle that Krenk had taught him in class, and he felt as if the world was isolated from him, like two parallel lines that would never intersect.

"Hey! Student! Say something!"

An anxious senior student grabbed the freshman's shoulder and pulled him back to reality.

The freshman looked at the countless expectant eyes around him, paused for a moment, and then immediately deflated.

He buried his face in his hands, looking dejected, and said in frustration, "I—can I say I didn't understand?"

"Um, what did Professor Klenk say in class?" a senior student asked, trying to find a better answer.

The freshman's face turned deathly pale, and he muttered in a daze, "Four-dimensional—Klein Magic Array—Bottle—The beginning is also the end—"

Everyone around couldn't help but look puzzled.

These few words are simply not enough to reconstruct what Krenk said in class.

Just then, the second freshman walked out of the teaching building.

Everyone crowded around again.

But to their surprise, the second freshman also looked desperate, didn't understand what Krenk was saying in class, and kept muttering incomprehensible new terms like Klein's magic circle.

One after another, the third and fourth freshmen also walked out of the teaching building, but without exception, they didn't quite understand what they were hearing.

But the only thing they agreed on was that their own level was too low, which was why they couldn't keep up with Professor Kroenke's line of thought.

All the senior students fell into deep thought and confusion, scratching their heads and relying solely on the freshmen's verbal descriptions to try and draw the four-dimensional Klein magic circle in their two-dimensional notebooks.

Further away, Abraham, dressed in a little evening gown with a rose tucked into his lap, stood by the window, watching the scene in front of the teaching building, and then turned around.

Looking at Krenk who had just entered the office, he asked curiously, "Professor Krenk, what did you study today? Why are all those students acting like this?"