How to break into a math book

In a plane, seven points are combined and arranged, and the triangle formed by any three points is required to have at least one side whose length is unit 1.This means that in all the triangles formed by these seven points, each triangle has at least one side of the same length.

According to this, the first thing Tu Hua thought of was circle.

On a graphic circle, the distance from the center of the circle to any point on the circle is equal, so as long as the length of the radius is set to unit 1, then the triangle formed by any two points on the circle and the center of the circle will inevitably form a side length of 1 isosceles triangle.

This question seems very intuitive, but the question stem gives an important constraint - there are 7 points in total.

According to Tu Hua's circle theory, one point of these seven points should be located at the center of the circle, and the remaining six points should be evenly distributed on the circumference, so that the six points on the circumference form an equilateral hexagon.

The six vertices of the regular hexagon are connected to the central point, and it can be clearly found that the hexagon is composed of six equilateral triangles, so as long as the side lengths of the six equilateral triangles are unit 6, then The triangle formed by two of them meets the conditions of the topic.

Tu Hua tried to piece together a regular hexagon with the seven star points next to it, but soon found that his idea was wrong.

If you ignore the center point and only look at the six vertices of the regular hexagon, as long as there are any two adjacent points, a triangle with a side of 1 must be formed.But if the three points of this triangle are not adjacent, that is to say, take a point every other vertex, the side length of this relatively large equilateral triangle is not equal to unit 1.

Therefore, this combined regular hexagon with at least one side as unit 1 cannot be completed, but the next best thing is a pentagon that can meet this requirement.

Because if you choose three of the five vertices of the pentagon to form a triangle, at least two vertices will be adjacent.As long as the side lengths of the pentagons are all unit 1, then the triangles formed by them must have a side length of 1.

But if you choose a pentagon, five vertices plus a center point... there are only six points in total.The requirement given by the title is that there are seven points in a plane, where can the extra point be placed?

Unknowingly, Tu Hua has fallen into a predicament.He swung the seven star points around in the air, but he still couldn't find a suitable combination.

There was nothing around, and no one could come to help him.

Tu Hua couldn't help recalling his terrible math results, as well as the help from his teammates and Su Gechi when encountering math problems in the previous levels.

He suddenly understood that this topic was a hurdle he had to go through.He was able to go to the end in "Mathematics Breakthrough". It is undeniable that he does have some cleverness, but more of it comes from the assistance of his teammates.His math grades are poor, so every time he encounters a professional math problem, he is always unable to do what he wants.When his teammates are around, someone will help him make suggestions, but in the end he will face this day alone.

So now he has to complete this topic independently.He not only needs to clear the level, but also proves himself that his math achievement is not his weakness, but a growing seedling. As he explores and comprehends the world of mathematics, this seedling will one day be able to shield him from the wind. rain.

He had to believe in himself. To be able to go so far in "Mathematics Breakthrough", his mathematics is not bad, but he just didn't find the direction.

Now... is the time for him to explore his direction.

Tu Hua looked at the vast void, and gently closed his eyes. The seven light spots in his mind, like the Big Dipper, were rapidly combining and changing, and each combination had been carefully calculated in his mind.

At least one side is equal...a pentagon...an equilateral triangle...

Tu Hua opened his eyes suddenly, enlightened instantly.Any three vertices of a pentagon can form a triangle with at least one side of length 1, but with the center point, there are only six points in the plane.

But... who said there can only be one central point?

As long as all the extra two points are placed inside the pentagon, the requirements expressed in the title can be completed!

Tu Hua hurriedly took the seven star points at hand, and began to assemble them in the air.His idea is very clear. Although the length of each side of this pentagon is unit 1, this pentagon cannot be a regular pentagon.

First, he used three points to form an equilateral triangle with a side length of 1, and then placed the fourth point under the equilateral triangle, so that these four points were connected to form an equilateral triangle consisting of two equal sides. A rhombus formed by stacking side triangles.

He still has three star points in his hand, as long as these three points can form an identical rhombus, and the outer five points form a pentagon, this sorting method can be established.

So the uppermost vertex of the second rhombus must be at the same point as the previous rhombus.

Tuhua uses the upper vertex of the first rhombus as the upper vertex of the second rhombus, and then bisects the included angle to make the two rhombuses coincide, so that the figure arranged with seven points looks like a five-sided five-sided figure from the outside. shape, and the interior of the pentagon has two points.

These two points are respectively the left vertex of No. 2 rhombus and the right vertex of No. 1 rhombus.

In the graphics combined by this method, any triangle combined with three points must have one side that shares the same side with the rhombus, that is, at least one side whose length is unit 1.

After Tu Hua arranged the seven dots neatly in order and angle, the seven light dots suddenly burst into colorful light.The next moment, the light absorbed Tuhua in.

In a blink of an eye, Tu Hua returned to the Rubik's Cube.

The red Rubik's cube color block under his feet has become a solid body, and he is sitting on the color block, and everyone is looking at him in surprise.Standing beside him, Shen Siyi quickly helped him up, and said pleasantly, "You're back, Tu Hua!"

Tu Hua quickly looked in the direction of the two girls who fell into the Rubik's Cube together with him, only to find that the color block they were in had become a solid body, but the two did not come back.

【Ding--】

[Challengers Liu Wei and Zhang Xiaoyu are eliminated. 】

Tu Hua was the only challenger to return from the Rubik's Cube after two turns.It takes a total of 13 steps to restore the Rubik's Cube, and after 3 steps, 4 challengers have been eliminated.

"So... what is in the Rubik's Cube?" Everyone looked at Tu Hua expectantly, hoping that he could give an answer.

Tu Hua explained the levels he experienced in the Rubik's Cube in detail. No matter how difficult it is, at least others have a bottom line in their hearts and know what they are about to face, which can be regarded as a preventive shot in advance .

Tu Hua felt that the problem he encountered was actually not difficult, but he was the only one of the five people who entered the Rubik's Cube world to come back. Either he was lucky, or the system had other tricks in setting the problem.Before I had time to think about the reasons, the next round of rotation was about to begin.

This time Rubik's Cube man designated the axis in the middle and turned it backwards twice.There were a lot of people on the middle axis, a total of five people, including Shen Siyi and Su Gechi.

Tu Hua couldn't help but feel a little nervous. After all, his two teammates are here. If something happens to the two of them in the Rubik's Cube, more than half of the help will be reduced in the next pass.He looked at Sugechi with some anxiety, but Sugechi gave him a reassuring look, and the five of them jumped into the depths of the Rubik's Cube together.

The waiting process was always anxious. About ten minutes later, Su Gechi's figure suddenly appeared on his original color block, and then Shen Siyi was also teleported back. Among the other three, there was only one girl returned, and the remaining two were directly eliminated.

There are only 18 people left in the original 12-player game, and they have not completed half of the steps to restore the Rubik's Cube.

Everyone present was depressed.Those who were lucky enough to escape from the Rubik's Cube had lingering fears, and those who had not yet experienced the turning were full of fear for the test they were about to face.

Rubik's Cube Man's face was pale, and the fourth rotation was about to start.He pointed at Tu Hua, his voice trembling: "Your row... turn around in a circle to the rear."

Tu Hua was the first person to fall into the Rubik's Cube for the second time. This time, there were more people with him, including two boys and one girl.The moment the ground under his feet vacated, Tu Hua skillfully closed his eyes, ready to face the next challenge.

After about five or six seconds, the feeling of weightlessness disappeared.Tu Hua returned to the dark void again, and there was still no human voice around.

【Ding--】

[How many parts can a 5D space be divided into at most by [-] planes? 】

The system screen was ejected in front of his eyes again. This time, the description of the topic was simpler than last time, and there were no auxiliary tools left. Tu Hua could only squat in the dark by himself and meditate with his brain.

He read the sentence in the title three times, and some thoughts flashed in his mind.Points can divide lines into several parts, and lines can also divide surfaces. In the same way, surfaces can divide cubes. This topic should belong to the category of solid geometry.

Tu Hua remembered that when they first learned geometry, the teacher once led them to study the law of dividing a plane with straight lines.When there is only one straight line, this straight line can only divide the plane into two, that is to say, the plane is divided into at least two parts, and at most it is divided into two parts.

But if a straight line is added on this basis, the way of division will deviate.This line can be parallel to the first line, or it can intersect it.Different segmentation methods can get different results. When two straight lines are parallel, the plane is at least divided into 2+1=3 parts. When two straight lines intersect, the plane is divided into 2+2=4 parts at most.

When three straight lines appear in the plane, inductive reasoning is carried out according to the method just now. The plane is at least divided into 4 parts, and the division method is that the three straight lines are completely parallel; at most, it can be divided into 2+2+3=7 parts. In the first two straight lines On the basis of the intersection, the third straight line intersects the two straight lines again, and the plane can be divided into 7 parts.

Carry out reasoning verification according to the mathematical induction method, assuming that there are n straight lines in total, it is easy to find that when the straight line divides the plane, the whole plane can be divided into 2+2+3+4+...+n=n(n+1)/ 2+1 parts, so put into the formula, 5 straight lines can divide a plane into 16 parts at most.

The rule summed up by this induction method is actually very simple.Because starting from the appearance of the third straight line, every time a straight line is added, the way to get the most division is to make this straight line intersect with every previous straight line, so the increased area is the area it passes through.

The area it passes through will be divided into two, and the increased part is the number of blocks passed through the area.This straight line has an intersection point with the original straight line on the plane, but the number of blocks it separates is exactly the number of intersection points plus one.This proves that when the nth straight line is added, the nth straight line has a total of n-1 intersection points with other straight lines, but it passes through n areas, dividing the plane into n more blocks.

There must be similarities between the two-dimensional space of the plane and the three-dimensional space of the cube.Tu Hua felt that he should use this law to inductively reason about the method of cutting a three-dimensional cube by a plane in three-dimensional space.

The intersection of a straight line and a straight line is a point, and the intersection of a plane and a plane is a straight line.

According to the reasoning result of dividing the plane by a straight line, assuming that n straight lines divide a plane into an part at most, then for a cube that has been divided into bn parts by n planes, add another plane, that is, the n+1th The first planes intersect with the previous n planes respectively, and the intersections between these n planes and the newly added plane are represented as n straight lines on this plane.

In the same way, the space area passed by this plane will also be divided into two, and the number of increased areas is the number of space areas it passes through, and this number is the number of blocks that divide this plane into n straight lines.

Therefore, when n planes have divided the three-dimensional space, the number of spaces increased by the newly added n+1th plane is exactly the number of planes divided by straight lines—a(n+1).

Tu Hua seemed to have been opened up to the two channels of Ren and Du, his brain spun rapidly, and soon deduced the calculation formula for how many pieces a cube can be divided into by n planes: (n^3+5n+6)/6.

Finally, combined with this question, the conclusion was drawn instantly: 5 planes can divide a cube into 26 parts at most.

The moment he answered, his body had already returned to the surface of the Rubik's Cube.

This proves his answer is correct.Tu Hua looked at the other challengers around in a daze. The two boys who went down with him also came back together, but the girl was eliminated directly.

The two boys were complacent, and told the people next to them that the question below was actually not difficult.

But Tuhua has a bad feeling.He obviously found that the second topic was much more difficult than the first one, and the topic changed from a simple two-dimensional combination to a thinking transformation of three-dimensional geometry.Although he answered all the answers in the end, if the difficulty continues to increase, he may not be able to do what he wants in the future.

No one found Tu Hua worried, and the game continued.The Rubik's Cube has turned 6 steps. According to Rubik's Cube Man's 13-step plan, there are still 5 steps left to complete the task of restoring the Rubik's Cube.

There are 11 challengers left on the field.

Rubik's Cube thought for a while, then pointed to the axis in the middle and said, "This face...turn forward once."

Shen Siyi and Su Gechi were still standing on the central axis, so this was the second time they had entered inside the Rubik's Cube.Besides the two of them, there were three other boys standing on the same side as them.

Everyone is already familiar with the rules of the game, and they are not too surprised that five people fell into the Rubik's Cube.But this time the waiting time was significantly longer than the last time. After about 20 minutes, Su Gechi and Shen Siyi were teleported back.

Unfortunately...the three boys were wiped out.

This was the time when the number of people lost was the largest, and everyone couldn't help but panic, asking Shen Siyi and Su Gechi what happened inside the Rubik's Cube.

Su Gechi frowned and thought for a while, then glanced at Tu Hua with a serious expression on his face: "Those three people... are not the first time to enter the inside of the Rubik's Cube."

Sure enough, Su Gechi's idea was exactly the same as Tu Hua's. The reason why the three boys didn't come out so easily was because after entering the Rubik's Cube for the second time, the difficulty of the game increased.

With their abilities, I'm afraid they won't be able to independently cope with games with increasing difficulty coefficients.Even after Su Gechi and Shen Siyi entered the Rubik's Cube for the second time, they were delayed for a long time.

Three people were directly eliminated in this round, and there are only the last 8 challengers left on the field, and it takes 4 more steps to solve the Rubik's Cube.If Tu Hua's reasoning is correct, as the number of times they enter the Rubik's Cube increases, the difficulty of the game will continue to increase, then the next four steps may not be so easy for them to pass.

As the commander, the Rubik's Cube man has not yet entered the Rubik's Cube. He looked at his feet with a pale face, and his voice trembled: "Next... the axis I am on, turn to the left once."

With his eyes closed, he lay nervously on the ground and followed the rotation of the Rubik's Cube. When the Rubik's Cube stopped, three people who were on the same plane as him fell down at the same time.

Rubik's Cube Man is the backbone of their Rubik's Cube recovery game. Although there are only the last three steps left, most people know how to take the next steps, but they don't want Rubik's Cube Man to be eliminated.

But things went against expectations, after waiting for a full half an hour, the Rubik's Cube man did not return to the surface of the Rubik's Cube until the white color block under his feet completely became solid.

【Ding--】

[Challengers Zhao Hai, Liu Lingling, and Wu Hongyu are eliminated. 】

The entire army was wiped out again, and there were three steps left to restore the Rubik's Cube, but only the last five people remained on the field.Tu Hua, Shen Siyi, Su Gechi, and a man and a woman who have each experienced a game.

The five people looked solemn.Everyone knows how to take the last three steps, but no one is willing to speak.

Su Gechi sighed, and looked at everyone: "The game has to continue. Then... the side under my feet, turn to the right twice."

The man and the woman happened to be on the same plane as Su Gechi. The girl was lying on the ground, looking very nervous.

Tu Hua was even more worried than she was.This is the third time that Su Gechi has entered the interior of the Rubik's Cube. No one can say for sure what he will encounter.He looked at Su Gechi's thin back, his lips trembled but he couldn't speak.

Su Gechi seemed to feel his gaze. One second before he fell into the Rubik's Cube, he suddenly turned around and looked at him softly: "Don't worry."

As the three fell into it, only Tu Hua and Shen Siyi were left on the surface of the Rubik's Cube.The two looked at each other without saying a word. After more than an hour, they still didn't come back.

Tu Hua always felt that in this [Geometry Rubik's Cube World], some important details were ignored by him.He looked at Shen Siyi and frowned: "You said... can we really clear the level if we recover the Rubik's Cube?"

Shen Siyi glanced at him, and said worriedly: "I've been thinking about this too."

"If we just let us pass the level, this ultimate level would be too easy." It was the first time that Tu Hua saw such an uneasy expression on Shen Siyi's face, and he speculated, "Mr. X also said, This geometric Rubik's Cube world is completely created by a virus, and the virus doesn't want us to pass the level at all, so how could it give us such an obvious way out?"

"Although for most people, it is very difficult to recover the Rubik's Cube within 20 steps, but as long as there is an answer, it proves that there is a way out. I always feel...these are all virus tricks."

Tu Hua nodded: "And... I always feel that there seems to be some connection between the levels we experience inside the Rubik's Cube..."

The two were just lost in thought when the system beeped suddenly:

【Ding--】

[Challengers Chen Ran, Bai Xinxiang, and Feng Shuhang are eliminated. 】

a bolt from the blue!Tu Hua quickly stood up, watching in disbelief that the transparent color block that originally belonged to Su Gechi's feet slowly became a solid body, and Su Gechi was eliminated? !

Shen Siyi also stood up, with a serious expression: "This is the third time he has entered the inside of the Rubik's Cube...so what is in the Rubik's Cube?"

Su Gechi can be eliminated, what kind of ghosts appear in the Rubik's Cube? !Tu Hua even wondered if this was Su Gechi's new strategy, and had no choice but to abandon the role of the challenger?

But no matter what the result is, at present, Su Gechi has been eliminated.Tu Hua and Shen Siyi are the last two left in the entire Rubik's Cube world, and they still have the most important step to recover the Rubik's Cube.

That is the side under Tu Hua's feet, which needs to be turned one last step before it can be completely returned to its original position.

Shen Siyi looked at him with a solemn expression: "No matter... what you encounter next, you just need to do your best."

Tu Hua couldn't help but look back and think about the past along the way. He has faced such an unknown world countless times, and he has also reined in the precipice of being eliminated countless times. In the game with 20 people, there were only two people left. They stood on everyone's shoulders and climbed to this position with difficulty.

If it fails, it will be completely lost.

Tu Hua vaguely felt that after completing this last step, he would be able to discover the ultimate meaning of the game world.Why Su Gechi was eliminated, what did the virus do, as long as he takes this last step, everything will have an answer.

He nodded at Shen Siyi, just like entering other levels before, without any reluctance or hesitation, with full of enthusiasm and confidence, he jumped into the nothingness of Rubik's Cube world.

This time the feeling of weightlessness lasted longer than the previous two.

Tu Hua didn't even know how long he had been floating in the void, he couldn't see anything, his body couldn't control his balance, and he became dizzy after a while.

In a daze, he seemed to have landed.He rubbed his eyes hastily, but saw something he had never imagined.

He saw the familiar classroom, and also saw him sitting in the bottom third row looking at the math teacher on the podium with his chin resting on his boredom. The large formulas on the blackboard were like a bible to him.Time seemed to be frozen, and he was like a spectator, seeing the sight of him in a math class on a certain day in the past.

Everything or everything in the scene is lifelike, but it is frozen like a wax figure.

Tu Hua stretched out his hand in a daze, before touching any entity, the scene in front of him suddenly changed.

This is his bedroom.Familiar light blue curtains, familiar desk lamps, stacks of review materials on the table.The wall clock on the wall showed the time as [-]:[-], and the second hand was fixed.

Tu Hua saw himself sitting in front of the desk. On the desk was a copy of "Mathematics Breakthrough". Holding a pen in his hand, he wrote the word "solution" behind a certain question.

Time seemed to stop at the moment before he entered "Mathematics Breakthrough". As a bystander, Tu Hua wanted to tell himself at that time, but before he could make a move, the scene changed again.

This time in the game, he was on a Pirates of the Caribbean ship with Sun Wei, Shen Siyi, Wang Boyu, and Tang Bo.Tu Hua looked at those former friends who had been eliminated, with mixed feelings in his heart.

The next moment, the scene changed again.This time, it is the scene where Tu Hua and Su Gechi express their hearts to each other in the [Desert Island Escape] level.Su Gechi's eyebrows and eyes were still as gentle as before, and it was the first time that Tu Hua saw his performance at that time from a third-person perspective.

With dazed eyes and a shy expression, it was the first time that he confessed to the person he likes, and his face was full of happiness.Although the picture is frozen, the sense of happiness can still be felt by Tu Hua now.

But in the next moment, Su Gechi, who was still motionless, suddenly glanced in his direction, and made a difficult mouth shape.

Tu Hua looked at him in astonishment, thinking that he was looking at everything he had experienced from the perspective of a bystander, why... Su Gechi can see him now?And he also said... "Run"?

The feeling of being in another world made Tu Hua finally wake up, his mind was immersed in the past world, and Su Gechi was reminding him.What he saw was just an illusion, the illusion that the system made him see when he fell into the Rubik's Cube World for the third time.

He suddenly came to his senses, the scene in front of him also disappeared, and the eyes returned to darkness.

Tu Hua remembered what Su Gechi had just said to him, and ran quickly.But running in the world of weightlessness seems to be a difficult thing. He struggled hard and alternated his legs at the fastest frequency before he could take a small step.

But just as he was running, the scene that had just disappeared reappeared.

Then the scene he saw just now was like a series of pictures frame by frame, forming a dynamic world.He saw the process of breaking through, saw his friends, and also saw Su Gechi.

In every frame of dynamic images, Su Gechi seems to want to break away from the original world and convey some kind of information to him.The faster Tu Hua ran, the stronger this feeling became.

He didn't care about admiring the old time he had passed, his eyes were fixed on Su Gechi, and his legs alternated rapidly.The scene in front of him also accelerated with his steps, like a time corridor, showing him all the plots quickly.

And on the way, Tu Hua saw the shadow of Su Gechi.

Su Gechi flickered in the rapidly changing images, Tu Hua couldn't hear his voice, he could only faintly see his mouth shape, and he said: "The exit is in the dimension of time."

The next moment, the scene in front of him freezes.

Tu Hua saw the geometric Rubik's Cube world, saw the huge Rubik's Cube that had been restored, and Shen Siyi who was anxiously waiting by the side.As if grabbing a life-saving straw, he rushed towards the world in front of him.

Finally, his body was sent back to Rubik's Cube World.

Everything around becomes real.Tu Hua was sweating profusely, kneeling in the center of the Rubik's Cube, panting.Shen Siyi quickly came over to help him: "Tu Hua! Are you okay? How is it?"

Tu Hua raised his head in a daze, looking at his teammates who were close at hand, he didn't even know how to describe what he just saw.

He saw himself in the past, and Su Gechi in the past.Or... the Suge Pool left behind in the cracks of time.

So Su Gechi was not eliminated, but stayed in the cracks to find a way out for them?What does he mean by "the exit is in the time dimension"?

Tu Hua felt a mess in his head, everything he experienced had completely surpassed his judgment and definition of this game.

The Rubik's Cube has been completely restored, but the two are still left in this Rubik's Cube world.The system seemed to be dead, and there was no news of customs clearance at all.

Shen Siyi supported him, and said in a deep voice: "It's good that you can come back. But... I think we may have no way to leave here."

Tu Hua frowned and looked at him, only to see Shen Siyi sighing: "The Rubik's Cube has been restored. According to the original regulations of the system, after the Rubik's Cube is restored, we should be able to clear the level. But obviously we were still put together by the virus. It didn't give us a chance to leave the game."

"Even if we complete all the levels, we can only wait here to die."

Tu Hua supported his forehead and sat on the Rubik's Cube, sorting out all the known information one by one.

First of all, although they completed the task of restoring the Rubik's Cube, the system did not allow them to pass the level.This proves that the virus did not prepare a way for them to pass the level. As Shen Siyi said, even if they completed all the level tasks, they could only wait here to die.

But... there is no exit, does it mean that there is no way to escape the game?

Just now inside the Rubik's Cube, the appearance of Su Gechi was no accident.With Su Gechi's ability, no matter how difficult the level of the virus is, he will never be eliminated. What's more, how could he allow himself to be eliminated when Tu Hua has not yet been found?

So Su Gechi should be using the name of elimination to find a way to leave the game world.He must have expected that the virus would not allow them to leave the level easily, and he had to enter the system to find a way to leave.

This is why he chose to sacrifice himself.The Suge Chi that Tu Hua saw just now inside the Rubik's Cube should have been the image of Su Ge Chi in the past, but he sent information to Tu Hua in an unexpected way.

The exit is just in the time dimension.

He can tell Tu Hua this sentence, it proves that he must have found a way to leave the game world.He was trying to think of a way to remind Tu Hua.

Tu Hua couldn't help but fell into deep thought, the dimension of time...what does the dimension of time represent?

He told what he had experienced inside the Rubik's Cube, and when Shen Siyi heard the words "time dimension", his expression became serious.

"Do you know super-dimensional space?" He looked at Tu Hua and hesitated.

Dimension is a term unique to astronomy and a very mysterious concept of physics.The mathematical geometry they understand actually has a certain relationship with these dimensions. "One-dimensional" represents points, and a collection of points forms a line; "two-dimensional" is a collection of lines, which is the scope often discussed in high school geometry— —Plane; as for "three-dimensional", it is a three-dimensional geometry represented by length, width, and height, which has one more vertical axis than the plane.

The world we live in is a three-dimensional world, so three-dimensional is the highest dimension that human beings can study.

Tu Hua has learned from various science fiction novels that there are high dimensions in the universe. The so-called high dimensions are dimensions beyond the limit of human cognition, and all above four dimensions are high dimensions.

The "four dimensions" that humans cannot explore, in addition to the three elements visible to the naked eye, length, width, and height, there is another dimension, that is-time.

Shen Siyi's reminder made Tu Hua faintly find some ideas. Could it be that what he just saw in the Rubik's Cube was the four-dimensional space?

He did go through the corridor of time, he saw his past, and even his future as long as he kept running.In that Rubik's Cube space, he did feel the existence of the time dimension.

"Higher dimensions are a collection of lower dimensions." Shen Siyi suddenly pulled Tu Hua's arm, his tone a little excited, "Points form lines, lines form planes, and planes form bodies! We in the three-dimensional world see worlds that are bigger than ours. A collection of one dimension lower."

"Although we are human beings in three-dimensional space, the objects we see will only be shown to us in a flat way, that is to say, what we see always has only one side, and we cannot see it from the same angle. Three-dimensional whole! This is the reason!" Shen Siyi explained, "So after you enter the Rubik's Cube world, even if you stand on the four-dimensional time, you can only see every time point in your life, and those are just the moments of your life. The section is the present moment!"

"So... so..." Shen Siyi paced back and forth, and suddenly became excited, "So as long as we can go to the fifth-dimensional space, we can jump out from here!"

"Five-dimensional space?!" Tu Hua looked at him in astonishment.

Shen Siyi nodded and continued to explain: "In the four-dimensional space, you can only see the point in time, but in the fifth-dimensional space, what you see is your entire life!"

Tu Hua finally understood the meaning of Su Gechi's sentence "The exit is in the time dimension".

The real multi-dimensional space-time is difficult for human beings to explore. The multi-dimensional they encounter here are only created by the system in the game.In fact, the virus did not completely block the exit, but gave them an opportunity that was difficult to find in three-dimensional space.They have to jump out of their understanding of the existing world in order to get out of the cracks in the system.

Tu Hua originally thought that the "time dimension" mentioned by Su Gechi was the four-dimensional space, but according to Shen Siyi's analysis, he had just gone to the four-dimensional space, and what he saw was only certain time points in his life. He just stands on the time axis and cannot escape time.

High dimensions are a collection of low dimensions, and only by standing in a dimension higher than time can we truly break away from the original timeline.If he can go to the fifth-dimensional space, he can fully witness his entire life, and then find the right time to escape from the current timeline.

But... how should he go to the fifth-dimensional space?

Tu Hua looked at Shen Siyi, and murmured: "Five-dimensional space... the first time I entered the interior of the Rubik's Cube, the system gave me a plane geometry problem. If divided according to dimensions, it should be a two-dimensional space; The second time I entered the Rubik's Cube world, the system gave me a three-dimensional geometry question, which should be three-dimensional space; the third time... When I entered the Rubik's Cube world, I was already in the four-dimensional space, standing on the time axis .”

"So... as the number of times you enter the Rubik's Cube increases, the dimensions you enter will also increase?" Shen Siyi touched his chin and asked in confusion, "But why did you enter directly into the one-dimensional space instead of the one-dimensional space for the first time?" What about two-dimensional?"

Tu Hua hooked his lips: "Because the dimension of time and space is not determined by the number of times you enter the Rubik's Cube, but depends on... the rotation of the Rubik's Cube."

Tu Hua lowered his head, looked at the huge crystal Rubik's Cube under his feet, squinted his eyes and said: "The first time the Rubik's Cube turned twice, so I entered a two-dimensional space, and the second time the Rubik's Cube turned once, then one dimension was increased. ...So, as long as I want to enter the five-dimensional space, I just need to turn the Rubik's Cube plane under my feet again."

Shen Siyi looked at the restored Rubik's Cube, frowned and said, "But if you turn it again, wouldn't the Rubik's Cube be unrestoreable?"

Tu Hua also felt that this seemed to be contrary to the original intention of the system, but for them now, there was no other better way, so he could only bite the bullet and try, maybe restoring the Rubik's Cube would only