I just want to be a quiet scholar

Chapter 69 Feel the fear of being dominated by geometry

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.

Mathematically speaking, this is not difficult to understand. Deriving proofs based on assumptions, or solving for the correct answer based on known conditions.

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

This is tactile geometry, Euclidean geometry, at least it looks.

The 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 happens when you extend two parallel straight lines wirelessly. I just take a high-speed train to go home for the New Year. The two rails under the high-speed train are in Does it matter to me whether it intersects 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 also called new geometry 200 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 obviously contradicts Euclidean geometry. In the standard of Riemannian geometry, any two railroad tracks that extend infinitely will one day intersect.

The classical significance 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 the earth civilization to communicate with it, communicate with it, work together, and Mutual benefit and win-win.As long as those civilizations promise to give up the research on the civilian technology of the two-way foil, everyone can be friends and build a beautiful home in the universe.

The perspective cuts from the vast universe back to the Milky Way-Orion Arm-Solar System-Earth-China Capital-Yenching University in a small dark room.

The reason why Shen Qi fell into contemplation was, what standard are the graphic questions on the blackboard based on, the Euclidean geometric standard or the non-Euclidean geometric standard?

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 extends the two sides AB and DE of the hexagon so that they 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, and 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 3 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 complement to Euclidean geometry.

"The picture on the left looks like a classic graphic expression of Pascal's theorem, then 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.

They, why do these three straight lines intersect at point L?
Is this a complete loss of conic section, or a perverted distortion of projection and truncation?
Euclid was obsessed with keeping the parallel lines for thousands of years and never intersecting. What is the point of the intersection at infinity with the knife behind Dezag?

However, when Lobachevsky threw out hyperbolic geometry, Master Riemann said with a faint smile that this is fucking bullshit, which is really embarrassing.

Behind a small blackboard, how many grievances and grievances are hidden?
Who will take over the fierce collision of old and new geometry in the red dust?
Can you feel the fear of being dominated by geometry?
Crack clap!

Shen Qi shreds the white paper in his hand, it's fake, it's all fake!
There is no solution to this problem, a fallacy!

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

It was clear that the sun was shining brightly when I left the dormitory early in the morning, but at this moment the sky was overcast.

Projective geometry shoots your uncle, the sun is extinguished by you, so today is Monday?

"It doesn't matter if he is on Sunday or Monday, we don't have to rest anyway. I'm hungry, so hungry, I'll be hungry when I do the questions, and I'll be even more hungry if I can't answer the questions." Shen Qi cooed with hunger, he just ate it an hour ago Breakfast, now hungry again.

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

Shen Qi rummaged through boxes and cabinets in the small room to find something to eat, but the result disappointed him. The only thing that could be eaten here, except for white paper, was books, and it was all spiritual food.

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

After a short period of irritability, Shen Qi forced himself to calm down, and he stared at the blackboard again. If it is based on 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 little black room alone. It's impossible for me to do such an obvious problem, right? Zhou Yuan can do this, he should be able to do it, right?"

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

Just thinking about it, the morning passed.

At twelve o'clock in the afternoon, there was a creaking sound, and the door of the small house opened. Sun Erxiong carried a thermos bottle in his left hand and a pot of vinegar in his right.

Putting the thermos and vinegar on the table, Sun Erxiong shouted in a tone of voice: "This little guest officer, here are the dumplings stuffed with chives and shrimps that you ordered."

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

"Hey hey, Shen Qi, don't destroy your young body like this. People are iron rice and steel, and if you don't eat a meal, you will be hungry."

Sun Erxiong lifted the lid of the thermos bottle and brought out the dumplings, which were steaming and fragrant: "Dumplings that just came out of the pot, why don't you eat a few of them. When can't you do the question, and you have to get along with your belly?"

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

"Whatever you want, you can." Sun Erxiong took out a few cloves of raw garlic from his pocket, smashed the garlic first, and then ate the dumplings for himself: "It's cool, it's cool, Shen Qi, you should eat the dumplings first. Don't be in a hurry."

"Are you still a professor of Buddhism?" Shen Qi picked up the chopsticks brought by Sun Erxiong, stuck a dumpling entrance, and chewed a few times.

"Why don't you dip your dumplings in vinegar, Shen Qi? If you don't dip them in vinegar and don't eat garlic, aren't you blind to 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 have to give me a standard, otherwise I can't do this question."

"Shen Qi, you have many advantages, but it is undeniable that you also have shortcomings, at least in mathematics. The mathematical knowledge and theories you have stored are too many and too complicated. Paranoia is more prone to internal injuries.”

"Oh, Professor Sun, I understand these big truths. Let's get the little things done first, and then we will discuss the big truths of mathematics proving in depth, okay?"

"Haha, let's eat dumplings, Shen Qi, until you order." Sun Erxiong smiled.

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

(End of this chapter)