Xiao Yu watched quietly, and this Luca toddler was still writing slowly.

"I've heard that Adults Three and Four are working on this. I've seen them on TV, and they're so powerful, it doesn't seem like it's hard for them to solve any problem. Only such a powerful character can become the master's right-hand man and get such great honors as No. 3 and No. 4. ”

"When I grow up, I must also become a scientist and take my parents and move to live in Paradise. I also want to have my own independent laboratory in the Eternal Kingdom, and become a great figure like Three and Four. ”

The Lucca toddler put down the pen, and at the same time, on the podium, the voice of the teacher came: "Okay, put down the pen, it's time to hand in the papers." ”

Several of the Lucca children stood up, took their positions, put away all the papers, and handed them to the podium. After the teacher announced the end of class, all the Lucca children ran out of the classroom laughing, but Xiao Yu still stared blankly.

At this moment, Xiao Yu's mind was turbulent.

Xiao Yu thought of a way, a way that was very likely to succeed.

"Mobius Ring? Möbius Ring? ”

As the Luca toddler said, the Möbius ring is made in a very simple way, as simple as a child of a few years old, just find a piece of paper and make it. However, in the Möbius ring, the truth contained in it is not simple.

When I was on earth, there was a joke about a Zen master that was widely circulated, which was that a young man went to consult a Zen master and asked about the weishenme above the shijie, and there was sadness in addition to joy. The Zen master asked the young man rhetorically and asked him, is there a paper on the shijie that only has the front and no tail?

In this joke, the young man brought a People's Daily, and was directly KO by the Zen master.

Of course, it's just a joke, even if you see it. But on shijie, there really is only one side of the paper, and that is the Möbius ring. - Just tear a slip of paper with your own hands, flip one end 180 degrees and merge the other end. Then with your finger along the Möbius loop, you can understand that it weishenme only one side.

In other words, there is no distinction between the inside and the outside of the Möbius ring. This is an important point.

Suppose you think of a two-dimensional shijie as a piece of paper, and draw a circle on this paper, and the circle becomes a cage for the two-dimensional shijie. In a two-dimensional shijie, you won't be able to escape this circle. Because it has no flaws. This circle is like a sphere in three shijie, and if you are imprisoned in a sphere, you will naturally have no way to get out - unless you pass through a dimension higher than this shijie, you can get out.

If you want to break through the blockade of a circle in the two-dimensional shijie, you can achieve the goal through the third dimension. If you want to break through a sphere in 3D shijie, you can pass through the fourth dimension.

However, the Möbius ring provides another way, that is, not to pass through the dimension higher than Benshijie. It is also possible to break through the blockade. In the two-dimensional shijie, you can turn this circle into a Möbius ring by distorting the space, because there is no difference between the inside and the outside of the Möbius ring, you just have to go out of a certain distance and then return the space to a level, and you will unknowingly get out of the blockade.

In a two-dimensional shijie, a circle can be broken through a Möbius ring, so is there a way to break through a sphere in a three-dimensional shijie?

After all, the Möbius ring is only suitable for two-dimensional space, and in two-dimensional space, the Möbius ring cannot exist, and it can only be made in a three-dimensional shijie that is one dimension higher than it.

So, is there something like a Möbius ring that can break through a three-dimensional sphere without going through the fourth dimension?

The answer is that such a thing exists, and that is the Klein bottle.

Suppose you have a vase with no bottom, and then you extend the mouth of the vase, bend it, let the mouth penetrate the bottle, enter the inside of the bottle, and place the mouth of the bottle where the bottle was originally the bottom, and it becomes a three-dimensional shijie Klein bottle.

The Klein Bottle is an upgraded version of the Möbius Ring. The Klein bottle made according to the above method is only a simplified version of the three-dimensional shijie, and the real Klein bottle cannot be truly manufactured in the three-dimensional shijie, just as the Möbius ring cannot be truly made in the two-dimensional shijie.

The mouth of a real Klein bottle does not need to penetrate the body to connect to the base. Because it is a product of the four-dimensional shijie, it is actually connected to the bottom of the bottle through the fourth dimension.

Like the Möbius Ring, the Klein Bottle is not inside or out. In other words, if you are inside a Klein bottle, you can go straight ahead without breaking through any blockade, and similarly, if you are outside a Klein bottle, you can go inside the bottle without hindrance.

"Morbius Ring, Klein Bottle!" Xiao Yu silently muttered these two terms in his mind, and began to calculate quickly unconsciously.

In order to make a Klein bottle, the following two conditions must be met. First of all, there must be an extremely deep understanding of the four-dimensional space, and secondly, it is possible to create a true four-dimensional space.

Xiao Yu couldn't create a four-dimensional space, but there was a four-dimensional space next to Xiao Yu—that four-dimensional barrier.

Then, there are only the following two points left for Xiao Yu to solve. One is the ability to bend three-dimensional space, which Xiao Yu has basically possessed through the research of faster-than-light travel. The second is the huge amount of energy required to bend space, and Xiao Yu has also obtained this ability through his deep study of elemental decay.

So, what is missing? Nothing is missing.

Xiao Yu began to get excited, and Xiao Yu keenly felt that he had found the right direction.

This method is in line with all of Xiao Yu's inferences.

The four-dimensional barrier is indeed too strong to be destroyed by a fourth-level civilization - the Klein Bottle can be crossed without destroying the four-dimensional barrier.

Only Xiao Yu can master it himself, and the rest of the fourth-level civilizations can't master it - the four-dimensional space is not accessible to the fourth-level civilization, and through getting along with Taihao during this time, Xiao Yu has obtained some relevant knowledge of the four-dimensional space, so he has the ability to make Klein bottles.

"There's a good chance that the Klein bottle is the key to unlocking the four-dimensional barrier...... So, let's start experimenting. At this moment, Xiao Yu made up his mind.

Xiao Yu glanced at the top of the stack of test papers on the podium in the classroom, and remembered the name of this Lucca child deeply in his mind, and then retracted his spirit.

"If you really break through the four-dimensional barrier through the method of the Klein Bottle, then you will become the fourth Lucca with a title, and you will become the Lucca Five."

Xiao Yu muttered to himself, and immediately gathered all the Lucca scientists to start a discussion in the auditorium.

Every Lucca scientist in attendance had a worried and haggard look on their face. Obviously, during this time, they did not think of the rest of the way, and none of them had a good rest.

"Master, I don't know what is the matter with you summoning us here?" Luca III asked.

"I have a guess." Xiao Yu replied, "I seem to have found a way to break through the four-dimensional barrier. ”

"Huh? What's the solution? What's the solution? Luca III asked eagerly.

"Klein bottle." Xiao Yu uttered a very short word.

In the auditorium, there was silence for a while. It seems that the four words of the Klein bottle have supreme magic power, which can make all Luccas fall into shock and be unable to extricate themselves.

"Klein bottles? Klein bottles? This kind of thing full of contradictions, really...... Can it help us? After a long silence, Luca III said this sentence with some difficulty.

The Klein Bottle is indeed a thing full of contradictions, and the paradox of it is that it simply cannot be truly made in 3D Shijie. But it is precisely these contradictions that give Xiao Yu a way to break through a sphere in the three-dimensional shijie.

"Don't forget, since you can break through the blockade of a two-dimensional circle in the two-dimensional shijie through the Möbius ring, then in the three-dimensional shijie, Weishenme can't break through the blockade of a three-dimensional sphere through a Klein bottle?"

Xiao Yu replied.

There was silence in the auditorium once again, and it was clear that the Lucca scientists were nervously thinking.

"Theoretically, well, I mean, it's perfectly feasible to break through the four-dimensional barrier through a Klein bottle just theoretically, but the question is, how do we go about making a Klein bottle that is full of contradictions? After all, we are in the three-dimensional shijie. Luca IV said.

"We have elemental decay jishu to provide energy, we have faster-than-light travel jishu to bend space, and we also have a four-dimensional barrier to provide us with a fourth dimension, so that we can connect the mouth of the Klein bottle to the bottom of the bottle without passing through the bottle body, and we can't make it?" Xiao Yu asked rhetorically.

"Well, that sounds like a lot of sense." Luca III said with some hesitation, "Anyway, this method is worth trying." ”

"Of course." Xiao Yu said, "We only have this one way left. If this method works, we can break through the four-dimensional barrier, and if this method is not feasible, we have no other way but to wait for death. So, let's start fighting. I need your help me to calculate the curvature and figure out how to make the Klein bottle......" (To be continued......

PS: Ask for a monthly pass! It's a little busy these days, and the rainbow will work hard to code words tomorrow or the day after tomorrow, and try to add more!