I Just Want to Be a Quiet Top Student

Shen Qi stayed in the room alone, moved a chair and sat down, facing the blackboard.

The topic left by Professor Sun is to supplement and improve the right picture based on the left picture on the blackboard.

From a mathematical logic point of view, it is not difficult to understand, deduce proofs based on assumptions, or solve the correct answer based on known conditions.

What is the picture on the left, a hexagon inside a circle.

This is palpable geometry, Euclidean geometry, at least it seems.

One problem with Euclidean geometry is that it always agrees with people's sense of touch, but not always with people's vision.

Of course, this problem is not a problem for more than 99% of human beings. Ordinary people don’t care what will happen if you extend two parallel straight lines wirelessly. I just take a high-speed rail home to celebrate the New Year. What does it matter to me whether they intersect under the definition of non-Euclidean geometry?

The opposite of tactile geometry is visual geometry. The former can be understood as Euclidean geometry, and the latter was called new geometry two hundred years ago. Lobachevsky and Riemann made the greatest contribution to new geometry. Today’s The non-Euclidean geometry mentioned includes Roche geometry and Riemann geometry.

Taking Riemannian geometry as an example, its core idea is that any two straight lines on the same plane must intersect.

This is obviously contradictory to Euclidean geometry. According to the standard of Riemannian geometry, if any two railroad tracks extend infinitely, they will intersect one day.

The classic meaning of Euclidean geometry cannot be denied. In the vast universe, any civilization that has mastered basic algebra, basic Euclidean geometry, and basic laws of low-speed physics is worthy of communication, communication, and hand in hand with the civilization of the earth. Mutual benefit and win-win. As long as those civilizations promise to give up the research of two-way foil civilian technology, everyone can be friends and build a beautiful homeland in the universe.

From the perspective of the vast universe, switch back to the Milky Way - the Orion Arm - the Solar System - the Earth - the capital of China - a small black room at Yenching University.

The reason why Shen Qi fell into deep thought was, what standard is the graphic topic on the blackboard based on, the standard of Euclidean geometry or the standard of non-Euclidean geometry?

Picking up a piece of white paper on the ground and a pencil on the table, Shen Qi drew a sketch on the white paper. He copied the circular inscribed hexagon on the blackboard.

Shen Qi extended the two sides AB and DE of the hexagon to make them intersect at point P.

Continue to extend BC and EF so that they intersect at point Q.

Extend CD, AF so that they intersect at point R.

Shen Qi connected the three points P, Q, and R. He muttered to himself: "The three points P, Q, and R are on the same straight line. This...is this Pascal's theorem?"

(Note [1] Pascal's theorem: If a hexagon is inscribed in a circle, then the three points obtained by the intersection of every two corresponding sides are on the same straight line.)

"So this is projective geometry?"

Shen Qi got the clue, but fell into deep thought again.

Projective geometry is not contradictory to Euclidean geometry, it is an important supplement to Euclidean geometry.

"The picture on the left seems to be the classic graphic expression of Pascal's theorem, so the picture on the right..." Shen Qi looked at the blackboard, and the picture on the right shows three straight lines intersecting at point L.

Why do these three straight lines intersect at point L?

Is this the complete loss of the conic section, or the abnormal distortion of projective and sectional views?

Euclid obsessively insists that parallel lines never intersect for thousands of years. Why is it that the intersection point is located at infinity when Dezag stabs his back?

However, when Lobachevsky threw hyperbolic geometry, Master Riemann smiled lightly and said that this is fucking bullshit, which is really embarrassing.

How many grievances and hatreds are hidden behind a small blackboard?

Who in the world of mortals will take over the fierce collision of old and new geometry?

Can you feel the fear of being dominated by geometry?

Click, click, click!

Shen Qi tore up the white paper in his hand, it was fake, it was all fake!

This question has no solution, fallacy!

Shen Qi scratched his head and fidgeted, he walked to the window and opened the curtains.

It was clear that the sun was still shining when we left the dormitory early in the morning, but at this moment the sky was overcast with clouds.

Projective geometry shot you uncle, the sun was turned off by you, so today is Monday?

"It doesn't matter if it's Sunday or Monday, we don't have a rest anyway. I'm hungry, I'm so hungry, I get hungry when I do the questions, and I get even hungrier if I don't do the questions." Shen Qi growled hungry. He just ate an hour ago. Breakfast, now I'm hungry again.

"Could it be that I activated some amazing foodie attribute?"

Shen Qi searched for food in the small room, but the result disappointed him. The only thing that could be eaten here was books, which were all spiritual food.

"Forget it, don't eat it, just bear it."

After a brief tantrum, Shen Qi forced himself to calm down. He stared at the blackboard again. According to the standard of projective geometry, there are many ways to complete the picture on the right, and there is more than one correct answer.

"But the fat old grandson called me to the small black room alone, so it's impossible for me to come up with such an obvious topic for me to solve, right? Zhou Yu'an knows how to do this, he should be able to do it?"

For some reason, Shen Qi couldn't concentrate, he was thinking wildly, he really wanted to eat a bear biscuit.

Just thinking about it like this, the whole morning passed.

At around 12:00 noon, the door of the small room opened with a creak. Sun Erxiong was holding a thermos in his left hand and a pot of vinegar in his right.

Putting the thermos and vinegar on the table, Sun Erxiong yelled in a tone: "Little guest officer, the dumplings stuffed with leeks and shrimps you ordered are here."

"I was quite hungry just now, I was hungry, I was hungry to the limit and I was full again." Shen Qi shook his head and said, "Professor Sun, eat dumplings by yourself. I haven't done this problem. I'm in a bad mood and I can't eat any more."

"Hehehe, Shen Qi, please don't ruin your young body like this. People are like iron rice and steel. If you don't eat a meal, you will feel hungry."

Sun Erxiong lifted the lid of the thermos bottle and brought out the dumplings, which were steaming and fragrant: "You can eat a few of the dumplings just out of the pot. When can't you do the problem, and you have to make trouble with your stomach?"

"Don't eat, don't eat, don't eat." Shen Qi shook his head like a rattle, never leaving his eyes from the small blackboard: "Professor Sun, at least give me some hints, under which geometric standard should I give the answer?"

"You can do whatever you want." Sun Erxiong took out a few cloves of raw garlic from his pocket, smashed the garlic first, and then ate the dumplings on his own: "Sweet, so cool, Shen Qi, you should eat the dumplings first. Don't rush things."

"Are you still a professor of Buddhism?" Shen Qi picked up the chopsticks that Sun Erxiong brought over, took a dumpling into his mouth, and chewed a few times.

"Why don't you dip your dumplings in vinegar, Shen Qi? You don't dip them in vinegar and you don't eat garlic, so you didn't lose sight of this pot of dumplings?" Sun Erxiong was very distressed, Shen Qi wasted a good dumpling.

"Oh, Professor Sun, stop talking nonsense, can we talk about something serious? Didn't you call me here to talk about mathematics with me, but I found that dumplings have become the protagonist of today. Hey, Professor Sun, it's crooked .You must give me a standard, otherwise I can't solve this problem."

"Shen Qi, you have many advantages, but it is undeniable that you also have shortcomings, at least in mathematics. The mathematical knowledge and theory you have accumulated is too much and complicated. If you do not have a strong self-consistent combing ability, it is too much Paranoia is vulnerable to internal injury."

"Oh, Professor Sun, I understand these big truths, let's get the small truths out first, and then go deeper into the big truths of mathematics, okay?"

"Hehe, let's eat dumplings, Shen Qi, order as many as you want." Sun Erxiong smiled.

"Eat, I'll eat!" Shen Qi threw away his chopsticks, grabbed a leek dumpling with his left hand and grabbed the dumpling with his right hand.