I just want to be a quiet scholar

Chapter 247 Non-Euclidean Geometry
Italian Fibonacci's mathematics level is a master level, and his translation level is a master+.

The hinterland of the Mediterranean where Italy is located connects Europe, Asia and Africa, where goods and knowledge from all over the world blend together.

Fibonacci, who is proficient in multiple languages, is the son of a Venetian merchant. He translated the mathematical literature of Egypt, Arabia, India, and China, and integrated them to form the European Renaissance Mathematical Encyclopedia.

As a result, European mathematics was revived. In the following hundreds of years, European mathematics geniuses emerged in large numbers, and mathematics entered the most prosperous golden age, and its far-reaching influence has continued to this day.

"Next I will get to know Luca Filbinotti." Shen Qi targeted a white boy with dark curly hair, thick eyebrows and big eyes. According to the information, Luca Filbinotti is an Italian student studying abroad. Among them, this boy is the only one with the appearance characteristics of southern Europeans.

The boy with dark curly hair and thick eyebrows raised his hand to indicate that he was Luca Philbinotti.

Shen Qi asked: "Luka, please tell me when the first math crisis happened and why."

"Around 400 BC, the root number 2 was discovered." Lucca recited the tone of the Greek epic in a tone, and performed a full role in the scene: "Everything is number, the universe can be measured, Hippasus, the king of evil host."

Yo, you can really act, have you studied at the Milan Drama Academy, Luca?

Shen Qi's acting skills were stimulated, and it was the first time he tutored students in a serious manner. He hoped to be able to mingle with these young lads.

"My dear friend." Shen Qi paced in front of Luca, slowly turning the pages of "Non-Euclidean Geometry" in his hand, he looked up at the ceiling, and stated in a Socratic tone: "Your words are biased." , my heart is at a loss, the square root of 2 is a reasonable existence.”

Lu Ka and Shen Qi looked at each other and smiled without saying a word.

These two drama masters, it really is a show!

The rest of the students did not expect Shen Qi to teach in this style, humorous and flexible, calm and magnanimous, much more interesting than those old men.

Shen Qi and Luca switched between the Greek epic painting style, and explained the first mathematical crisis with questions and answers.

The Pythagoreans believed that "everything is number", and they believed that everything in the universe is commensurable, which is expressed as the ratio of two integers.

The appearance of the square root of 2 made Pythagoras terrified. This evil number could not be expressed as the ratio of any two integers!

Does not exist, root sign 2 or evil numbers similar to root sign 2 absolutely do not exist.

However, Hippasus, a student of Pythagoras, successfully proved the existence of the root number 2, and the concept of irrational numbers was born.

"Irrational" is irrational relative to rational numbers, and irrational numbers themselves are reasonable.

This is the mathematical crisis that occurred more than 2000 years ago. It was caused by the root number 2 and irrational numbers. It is called "the first mathematical crisis" in history.

"I'm very satisfied with Luka's answer." Shen Qi walked back to the blackboard and said, "Equivalent exchange, I will announce my age information. I am 21 years old this year, and I will turn 22 in a few months."

"God, I'm also 21, and I'm still in the second grade!" Stephen yelled exaggeratedly, there is no harm without comparison.

"Stephen, Uncle Colorado, when you were 23 years old and in the fourth grade, Qi, who was also 23 years old, might become your thesis advisor." Luca boldly predicted such a situation.

Luca is 19 years old this year. Youth represents hope. He has more potential and age advantages than those old guys over 20 years old.

"Super verbose Italian!" Stephen came from a small fifth-tier city in Colorado, and was one of the few native American students in the class.

Although 90% of Princeton's undergraduates come from the United States, the exception is the Department of Mathematics, where more than half of the undergraduates in the Department of Mathematics are foreign students.

"The exchange of the history of mathematics belongs to the extended training, and it is not included in the evaluation report of the tutorial course." Shen Qi entered the topic freely. The history of mathematics is the appetizer, and non-Euclidean geometry is the main meal.

The atmosphere of the topic became serious and relaxed for a while. In the end, the 21-year-old teaching assistant brother still wanted to play for real.

The professor of the major class is responsible for explaining the basic theories, and the teaching assistant of the tutorial class is responsible for guiding the students to review, assign homework, and check the homework.

After going through a series of tests such as lectures, tutorials, participation in group discussions, completion of assignments, and exams, these second-year students can receive credit for a course.

Princeton has more teachers and fewer students, and they have the best undergraduate education in the world.

University students are under a lot of pressure and work hard, but the students who have received this high-level and high-quality education have a unique style and temperament after they leave the Princeton school.

The employment rate of Princeton undergraduate graduates is as high as 94%, which can be described as "produced by the general university, which will be hard to find" in the United States where the unemployment rate is so severe.

Shen Qi entered the topic and started the tutorial. He also started with a professional question: "John M. Groston, please answer me in one sentence. What is the difference between non-Euclidean geometry and Euclidean geometry? I think Muller The professor has already taught you, let's review this most basic concept."

John M. Gloston from England replied immediately: "In Euclidean geometry, if a line intersects two other lines such that the sum of the interior angles on one side is less than two right angles, then the two lines are on that side. must intersect when extended. And in non-Euclidean geometry..."

Shen Qi interrupted John-M-Grosston's answer, and shook his head dissatisfied: "Hey, John, I don't want to hear the fifth postulate of Euclid without changing it, which is a passing grade for middle school students." Standard. And you, John M. Gloston, are a sophomore in Princeton's math department. I need more creative answers."

"Jack-Ma, please continue to answer this question." Shen Qi focused on a student with an Asian face. He remembered that there was a student named "Jack-Ma" on the student roster, and his nationality was American.

The name Jack-Ma is Asian at first glance, and there is a high possibility that it is Chinese.

Sure enough, this young man with an oriental face was Jack Ma. He was not tall, with dark skin and a fashionable hairstyle.

Jack Ma gave his answer, speaking pure American English, explaining that he has lived in the United States for a long time, and he should have grown up in the United States: "The spherical surface in Euclidean geometry, for the ants crawling on the spherical surface, Speaking of the plane of non-Euclidean geometry, ants will not feel the curvature of the sphere during crawling."

Shen Qi snapped his fingers, very satisfied with Jack-Ma's answer: "Hey, hey, Jack, Jack, perfect answer, A+! This is Princeton's style."

"Hey hey, yes, thank you for the compliment." Jack Ma was not at all humble and polite after receiving the praise. It seems that he has been deeply influenced by American culture.

After entering the classroom, Shen Qi quickly asked a few questions, including two questions about the history of mathematics and several questions about non-Euclidean geometry. Each of the twelve students accepted Shen Qi's questions.

Shen Qi memorized the faces of every student in the tutorial class, and took his seat according to the English name on the roster.

Currently, the best performers are Italian student Luca and Asian American Jack Ma.

Excellent students always get more attention from the teacher. Shen Qi changed his role unconsciously, and his first tutorial class was considered a success.

At least so far, twelve second-year students in the mathematics department have given favorable comments to Shen Qi, the tutor teacher.

With a class fee of US$120, Shen Qi earns easily and comfortably. He likes this classroom atmosphere. He hopes to share some of his mathematics experience and knowledge with these juniors and help them.

Heated discussions and expressing one's views are the main theme of the tutorial class, and there will be a brainstorming session from time to time to conduct divergent logical deduction on a certain topic.

The topic of the Department of Mathematics is often a math problem. Shen Qi, who started his career by brushing up questions, no longer does it. He is responsible for formulating questions and assigning homework.

(End of this chapter)