"Actually, it is not used to study how much water it can hold. It is used to study the plane." Gu Qing continued, "We all know that things have two sides, one piece of paper has a front and a back, but this Klein bottle has only one side, so it was used to study the face at the beginning."

"I didn't understand." Gu Xiao shook his head vigorously.

Gu Qing tore a piece of paper and twisted it into a ring and said to Gu Xiao, "Now look at how many sides this piece of paper has."

After watching for a while, Gu Xiao found that his expression was very confused. No matter how he walked along this twisted trajectory, he would go to the original point. "This seems to have two sides, it seems to have only one side, it is so magical."

"This is called the Mobius ring." Gu Qing then made a Mobius ring again. After the two were connected in parallel, they looked like a Klein bottle. Then he said, "The Mobius ring is a research area, and this Klein bottle is used to prove the Mobius ring. In fact, the Klein bottle in my hand is wrong. It can be filled with water, because the real Klein bottle cannot be made in this world. If it really exists, it only exists in four-dimensional space."

"What is four-dimensional space?" Gu Xiao continued to ask.

"Four-dimensional space is a space that transcends our place, and our space is a three-dimensional space." Gu Qing continued, spreading a piece of paper and saying, "This piece of paper is a two-dimensional plane. We can easily draw a circle on it. At that time, because we are in three-dimensional space, if we are in four-dimensional space, it is as simple as drawing a circle on the two-dimensional plane of three-dimensional space."

"A long time ago, there was a woman who many people thought she could spell because she could take down the heart of one of the people in another place. Many people thought it was magical. After that, the woman's ability could no longer be used. That was because she briefly contacted a fragment of a four-dimensional space. Just as it was easy for us to draw a circle on a two-dimensional plane in a three-dimensional space, she could also do it easily." Gu Qing looked at his son and said, "You think it is a story. The existence of four-dimensional space has always been a mystery, and it is also a puzzle left by thousands of years of human beings. No one can solve this puzzle. Perhaps the vast universe, that is, what they said, may have an answer."

"And this Mobius ring is an argument for rising from two-dimensional to three-dimensional." Gu Qing continued, "and this Klein bottle is used to argue the argument for rising from three-dimensional to four-dimensional space. However, we live in three-dimensional space and we cannot make bottles that are not full of water in our hands."

"Oh." Gu Xiao nodded vigorously, and a puzzle was in his heart at this moment.

Gu Qing said again, "The puzzle you gave to Li Chunfeng is, when a piece of paper with two sides became a ring of Mobius, why did there be only one side? Where did the disappearing side go? And this bottle, is it another side, three sides or four sides?"

Gu Xiao was very interested in holding the Mobius ring. After repeated trial and error, he did indeed return to the origin no matter which point he started. After a piece of spread paper was twisted and spliced, he actually had such a mysterious smile and said, "If you don't know the relationship between two-dimensional three-dimensional and four-dimensional, Li Chunfeng would probably be crazy."

"You." Gu Qing poked Gu Xiao's forehead, "Don't mess around in the academy. Listen to the masters, don't get too close to this guy Li Chunfeng. This old guy also likes to study some things that are strange and chaotic. You are not allowed to follow him."

"I understand, I wasn't interested in those things." Gu Xiao said, holding the Klein bottle.

After walking out of the laboratory, Gu Xiao was still confused. After dinner, he came to Gu Qing and asked, "Father, what would it be like if we could enter the four-dimensional space."

"Four-dimensional space?" Gu Qing looked up at the starry sky, "We can't get into it. If we enter the four-dimensional space, it is transcending beyond time. Time is a dimension in the four-dimensional space."

"Oh." Gu Xiao also looked up at the starry sky.

Early the next morning, Gu Xiao returned to the academy. Zhang Jiuling saw Gu Xiao coming back at the door of the academy and hurried forward, "Gu Xiao, have you found the question?"

"Finished." Gu Xiao said confidently with the Klein bottle.

"Why forget it, just apologize to Master Li Chunfeng." Zhang Jiuling said, "Buddie Li Chunfeng is a master of mathematics in the academy, and your questions will not be difficult for him."

"Do you know who my father is?" Gu Xiao said confidently, "Brother Zhang! I heard from my master's grandfather that Master Li Chunfeng had to ask my father for advice when my father was a child? Don't worry, I won't lose."

"I know your father is Gu Qing." Zhang Jiuling sweated coldly.

"I will apologize for an apology, but apology and competition are different things. I will not lose to him, Li Chunfeng." Gu Xiao strode into the academy and came all the way to Li Chunfeng's office.

Zhang Jiuling followed him here and hurriedly saluted Li Chunfeng, "I have met Taoist Master Li Chunfeng."

"Little kid, have you found the question?" Li Chunfeng looked at Gu Xiao.

"Yes, I found the question." Gu Xiao said, "Master Li Chunfeng, it's still time for you to admit defeat now."

"Give up? Haha!" Li Chunfeng sneered, "Let's make a question."

"Okay!" Gu Xiao took a piece of paper and said, "Master Li Chunfeng is right. Is this a piece of paper right? Is this piece of paper right? Isn't it right?"

"Yes." Li Chunfeng nodded.

"Whether Master Li Chunfeng believes it or not, I can let the other side of this piece of paper disappear."

Listening to Gu Xiao's words, Li Chunfeng sneered, "How is that possible, unless I am blind."

"Then you're good." Gu Xiao used the paper in his hand to splice the head and tail according to the method Gu Qing taught yesterday. After the sticking, a Mobius ring was done. "Okay, now Master Li Chunfeng looks at this ring made of paper, and there are several sides."

Li Chunfeng curiously took the ring made by Gu Xiao and said, "Even if you connect the first part of the paper together, there will be two sides, and one side cannot disappear."

"If it is two sides, you won't bump into the two points when they are separated. Take a look." Gu Xiao sat in front of Li Chunfeng with an old man.

Li Chunfeng observed the Mobius ring in his hand. After several observations, he found clues. He looked at Gu Xiao in surprise, then took out the brush and chose a point from Mobius to start moving along the way until he returned to the starting point. Li Chunfeng was so shocked that he didn't hold the brush in his hand.
Chapter completed!