I Just Want to Be a Quiet Top Student

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

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

　　 It is not difficult to understand mathematically and logically. Proofs can be derived based on hypotheses, or the correct answer can be solved based on known conditions.

　　 The picture on the left is a gadget, a circle with a hexagon inside.

　　 This is the geometry that can be touched, that is, Euclidean geometry, at least it looks like this.

　　 There is a problem with Euclidean geometry. It is always consistent with people's sense of touch, but not always consistent 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 rail home to celebrate the New Year. The two rails under the high-speed rail car are in Does intersect under non-Euclidean geometry definition have anything to do with me?

The opposite of tactile geometry is visual geometry. The former can be understood as Euclidean geometry, while the latter was called the new geometry two hundred years ago. Lobachevsky and Riemann have made the greatest contributions to the new geometry. The non-Euclidean geometry includes Roche geometry and Riemannian geometry.

　　 Take Riemannian geometry as an example. Its core point 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, any two railroad tracks that extend indefinitely will meet one day.

It is impossible to deny the classical meaning of Euclidean geometry. 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’s civilizations to communicate with each other, to communicate with each other, and to make progress together. Mutual benefit and win-win situation. As long as those civilizations promise to abandon the research of two-way foil civilian technology, everyone can be friends and build a beautiful home in the universe.

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

　　 The reason why Shen Qi fell into contemplation is, what standard is the graphic title on the blackboard based on, Euclidean geometry standard or non-Euclidean geometry standard?

　　 picked up a piece of white paper on the ground, picked up a pencil on the desk, and Shen Qi drew a draft 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 and AF so that they intersect at point R.

　　 Shen Qi connects the three points of P, Q, and R, and he muttered to himself: "The three points of 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, 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 inconsistent with Euclidean geometry, it can be regarded as an important supplement to Euclidean geometry.

　　 "The picture on the left looks like a classic graphical 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 the complete loss of the conic section, or the perverted distortion of the projection and the scene?

　　 Euclid obsessively guarded the thousand-year parallels and never intersect. Why is the intersection at infinity when Dezag is inserted behind his back?

　　 No matter how Lobachevsky throws out hyperbolic geometry, Master Riemann said with a faint smile and said that it was all **** shit, it was really embarrassing.

　　 Behind a small blackboard, how many grievances and hatreds are hidden?

　　Who in the red dust 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 blank paper in his hands, fake ones, all fake ones!

　　 There is no solution to this question, fallacy!

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

　　 When I leave the dormitory early in the morning, the sun is still shining, but now the sky is full of clouds.

　　 Projective geometry shoots you uncle, the sun was shot out by you, so today is Monday?

"It doesn't matter if he is Sunday or Monday, we don't have to rest anyway. Hungry, so hungry, I will be hungry as soon as I do a problem, and even hungry if I can't do it." Shen Qi grumbled, he had just eaten an hour ago Breakfast, now hungry again.

　　 "Could it be that I activated some of the incredible food properties?"

　　 Shen Qi rummaged in the small room looking for food, but he was disappointed. The only thing he could eat here except for the white paper was books, it was all spiritual food.

　　 "Forget it, stop eating, forbearance."

　　 After a brief irritability, Shen Qiqiang exercised himself to calm down. He stared at the blackboard again. If it is under 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 sun called me to the little black room alone. It's impossible to give me such an obvious question? Zhou Yuan can do this, he should be?"

　　 I don't know why, Shen Qi can't concentrate, he is thinking about it, he really wants to eat a bear biscuit.

　　 Just thinking like this, the whole morning passed.

　　 After twelve o'clock at noon, there was a creak and the door of the small room opened. Sun Erxiong carried a thermos in his left hand and a pot of vinegar in his right. He hummed a small song from the northeast couple and entered the house leisurely.

　　 Put the thermos and vinegar on the table, and Sun Erxiong yelled, "The little guest officer, you have dumplings with chives and shrimp stuffing."

　　 "I was very 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 topic. 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 but steel. UU reading www.uukanshu.com will panic if you don't eat a meal."

　　 Sun Erxiong uncovered the lid of the thermos bottle and brought out the dumplings. The aroma was steaming and scented: "You just have to eat a few dumplings that have just come out of the pot, how about you eat a few. When can't you do it? I have to have trouble with my belly?"

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

"Whatever you want." Sun Erxiong took out a few cloves of raw garlic from his pocket, knocked a piece of garlic first, and then took a bite of dumplings on his own: "Cool, really cool, Shen Qi, you can eat dumplings first. Don't worry about things."

　　 "Are you still a professor of Buddhism?" Shen Qi picked up the chopsticks Sun Erxiong had brought over, put a dumpling in the mouth, and chewed it a few times.

　　 "Why don't you eat dumplings with vinegar? Shen Qi? If you don't eat dumplings with vinegar and garlic, you won't be blind to this pot of dumplings?" Sun Erxiong was very distressed, and Shen Qi wasted a good dumpling.

"Oh, Professor Sun, stop talking, can we talk about something serious? Didn't you call me to talk about math with me, but I found that dumplings have become the protagonist of today. Hey Professor Sun, it’s awkward. . You must 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 reserve are too many and too complicated. If you do not have strong self-consistent combing ability, it is too much. Paranoia is prone to internal injuries."

　　 "Oh, Professor Sun, I understand these principles. Let's get the basic principles first, and then discuss the principles of mathematical proofs, okay?"

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

　　 "Eat, I will eat!" Shen Qi dropped his chopsticks and grabbed a leek dumpling in his left hand and right hand.