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

Professor Sun's project is to supplement the right picture based on the left picture on the blackboard.

Mathematically speaking, it is not difficult to understand that proofs can be derived based on assumptions, or correct answers can be solved based on known conditions.

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

This is the geometry that can be touched, the Euclidean geometry, at least it seems.

One of the problems with Euclidean geometry is that it is always consistent 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 your two parallel straight lines extend wirelessly, I just take a high-speed train home for the New Year, and whether the two rails under the high-speed rail carriage intersect under the definition of non-Euclidean geometry What does it matter to me?

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

In the case of Riemannian geometry, for example, the central idea is that any two straight lines on the same plane must intersect.

This is obviously a contradiction to Euclidean geometry, in which any two railroad tracks that extend infinitely will one day intersect.

The classical significance of Euclidean geometry cannot be denied, and in the vast universe, any civilization that has mastered the basic algebra, basic Euclidean geometry and basic laws of low-speed physics is worthy of communication and communication with the earth's civilization, mutual exchange, hand in hand, mutual benefit and win-win results. 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 home for the universe together.

The perspective cuts back from the vast universe to the Milky Way - Orion's spiral arm - the solar system - Earth - the capital of China - in a small dark room at Yenching University.

The reason why Shen Qi fell into contemplation was that the figure titles on the blackboard were based on what standard, Euclidean geometric standard or non-Euclidean geometric standard?

Picking up a piece of white paper on the ground and copying a pencil on the table, Shen Qi drew a sketch on the white paper, and he copied the circle on the blackboard with a hexagon.

Shen Qi extends the two sides of the hexagon, AB and DE, so that they intersect at point P.

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

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

Shen Qi connected the three points of P, Q and R, and he muttered to himself: "The three points of P, Q and R are in the same straight line, this ...... Is this Pascal's theorem?"

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

"So this is projective geometry?"

Shen Qi got the clue, but fell into contemplation again.

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

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

Why do these three lines intersect at point L?

Is this the complete loss of the conic curve section, or the perverted distortion of projections and shots?

Euclid obsessively guards the thousand-year-old parallel lines that never intersect, what is the reason why Dezag sticks a knife behind his back and the intersection is located at infinity?

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

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

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?

Click, click, click!

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

There is no solution to this problem, fallacy!

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

The sun was still shining when I left the dormitory early in the morning, but the sky was cloudy at the moment.

Projection geometry shot your uncle, the sun was shot out by you, so today is Monday?

"It doesn't matter if it's Sunday or Monday, we don't have a break anyway. I'm hungry, I'm hungry, I'm hungry when I do the question, and I'm even hungrier if I can't do the question. Shen Qi cooed with hunger, he had just eaten breakfast an hour ago, and now he was hungry again.

"Could it be that I've activated some awesome foodie attribute?"

Shen Qi rummaged through the boxes and cabinets in the small room to find food, but the result disappointed him, the only thing he could eat here was all spiritual food except for blank paper and books.

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

After a short period of irritability, Shen Qi forced himself to calm down, he stared at the blackboard again, if it is under the standard of projective geometry, there are many ways to solve and 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 house alone, it is impossible for me to come up with such an obvious topic, right?

For some reason, Shen Qi's concentration couldn't be concentrated, he was thinking about everything, and he really wanted to eat a bear biscuit.

Just thinking about it, the morning passed.

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

Putting the thermos flask and vinegar on the table, Sun Erxiong shouted in a tone: "This little guest officer, the dumplings stuffed with leeks and shrimp you ordered." ”

"I was very hungry just now, hungry and hungry, hungry to the limit and full again. Shen Qi shook his head and said, "Professor Sun, you can eat dumplings by yourself, this topic has not been made, I am in a bad mood and can't eat it." ”

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

Sun Erxiong lifted the cap of the thermos bottle and brought out the dumplings, steaming and fragrant: "The dumplings just out of the pot, how about you eat a few, when can't you do it, you have to get along with the belly?"

"Don't eat, don't eat, don't eat. Shen Qi shook his head like a rattle, and his gaze never left the small blackboard: "Professor Sun, why don't you give me some hints, and 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 garlic first, and then ate dumplings by himself: "Cool, really cool, Shen Qi, you eat dumplings first, don't be anxious about doing this kind of thing." ”

"Are you still a Buddhist professor?" Shen Qi picked up the chopsticks brought by Sun Erxiong, took a dumpling into his mouth, and chewed it a few times.

"Why don't you dip dumplings in vinegar Shen Qi? If you don't dip 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, don't talk nonsense, can we talk about something serious? Didn't you call me to talk to me about mathematics, but I found that dumplings have become the protagonist today, hey Professor Sun, it's crooked. You have to give me a standard, or I won't be able to do it. ”

"Shen Qi, you have many advantages, but it is undeniable that you also have shortcomings, at least in mathematics. You have too many mathematical knowledge and theories, and if you don't have a strong ability to sort out self-consistently, you will be too paranoid and prone to internal injury. ”

"Oh, Professor Sun, I understand these big truths, let's get the small ones right first, and then delve into the big truths of mathematical preaching, okay?"

"Hehe, eat dumplings Shen Qi, order until you arrive. Sun Erxiong smiled.

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