The word "ancient Greece" is familiar to us, but many people don't understand it.
If Euclid, the author of Elements of Geometry, can represent the whole ancient Greek people, then I can say that ancient Greece is the most brilliant branch of ancient culture-because mathematics in ancient Greece not only contains mathematics, but also contains rare logic and intriguing philosophy.
The mathematical work Elements of Geometry is connected with several obvious and well-known definitions, postulates and axioms, and develops a series of propositions: from simple to complex, they complement each other. We have to admire its rigorous logic.
Judging from the proposition I have visited so far, Euclid proved that the most common and basic problem about the "equal length" of line segments is to draw a circle: because all radii of a circle are equal. General mathematical thinking is very complicated. Just a little bit here, and then I went there again. The Elements of Geometry is easily accepted by me, probably because Euclid repeatedly used an idea to make readers accept it.
But what I want to emphasize is his philosophy.
There are several propositions in the book: for example, "the two base angles of an isosceles triangle are equal, and the two complementary angles formed by the waist and the base are equal", and for example, "if the two angles in a triangle are equal, then the two sides are equal". When I read these propositions, I have been suffering from shocks outside geometry.
We studied geometry in the seventh grade. When we thought of doing this kind of proof and needed to prove that the two angles in a triangle were equal, we always wrote: "Because it is an isosceles triangle, the two base angles are equal"-we always habitually think that the two base angles of an isosceles triangle are equal; While reading "The Elements of Geometry", he thought about "why the two base angles of an isosceles triangle are equal". Think about it, a thought is habit, and a thought is thinking about why. Isn't this enough to explain the problems of modern people?
Most modern people seem to have lost their curiosity. Curiosity here refers not only to the kind of interest in novelty, but also to ordinary things. For example, many people will ask "why do astronauts float in the air", but they may not ask "why can we stand on the ground and not float"; Many people will ask "What can you eat to lose weight", but they may not ask "Why do sheep eat grass instead of meat".
We are so used to the things around us that we are not interested in many "ordinary" things and then think about them. Why did Newton discover gravity? A large part of the reason lies in his curiosity.
If we just read the Elements of Geometry as a math book, it would be a big mistake, because ancient Greek mathematics is permeated with philosophy, and learning mathematics is learning philosophy.
The first lesson of philosophy: people should be curious, not only to explore new things, but also to explore ordinary things around them. This is my windfall from reading the Elements of Geometry!
Selected Works of Geometry Original Reading 2 Geometry Original is an immortal work of Euclid, an ancient Greek mathematician, which combines the achievements and spirit of ancient Greek mathematics. It is not only a masterpiece of mathematics, but also a masterpiece of philosophy, which completes the human understanding of space for the first time. This book has been translated and revised for more than two thousand years since its publication. Since 1482 was first printed and published, there have been more than 1000 different versions.
There are no other works except the Bible, and its research, use and dissemination can be compared with the Elements of Geometry. The earliest Chinese translation was completed by Italian missionary Matteo Ricci and Ming Dynasty scientist Xu Guangqi in 1607, but they only translated the first six volumes. It is proved that this manuscript determines the basic terms of modern mathematics in China, such as triangle, angle and right angle. Japanese, Indian and other eastern countries all use China's translation, which is still in use today. In the past hundred years, this masterpiece has been mentioned in Chinese mainland's middle school textbooks, but for China readers, it has been neglected to see its whole picture, and it is wishful thinking to include it in family books.
Xu Guangqi spoke highly of this book when he translated it. He said, "whoever can master this book can do anything." People who are eager to learn this book are unscientific. "Einstein, the founder of modern science, even thought that if Euclid failed to arouse your scientific enthusiasm in your childhood, you would certainly not become a talented scientist. It can be seen that geometric elements have a great influence on people's rational deductive ability, that is, on people's scientific thinking.
As long as people who have attended junior high school have studied geometry, they may not know that Xu Guangqi, a great scientist in the Ming Dynasty, and Matteo Ricci, an Italian missionary, introduced geometry to China, let alone that Xu Guangqi creatively translated geodesy into geometry. It has been 400 years since 1667 translated the first six volumes of Elements of Geometry.165438+/kloc-0 held various commemorative activities in Shanghai and other places on October 9. More than 60 Chinese and foreign scholars from nine countries, including Italy, the United States, Canada, France, Japan, Belgium, Finland, the Netherlands and China, and four places on both sides of the Taiwan Strait gathered in the resting place of Xu Guangqi in Xuhui District to commemorate the 400th anniversary of the translation and publication of Xu Guangqi's Geometry.
"It is a shame for a Confucian to know nothing."
Xu Guangqi's family is ordinary, and his father is an unsuccessful businessman. After bankruptcy, he worked as a farmer in Shanghai and his family was poor. Xu Guangqi/KLOC-Jinshi at the age of 0/9. It took 16 years to rise to the position of scholar, and then it took another 7 years to be a scholar. When he participated in the selection of imperial academy, he ranked fourth, that is, he was selected as Jishi Shu of imperial academy, equivalent to a doctoral student of the Royal Academy of Sciences in the Ming Dynasty. He ranked 52nd among the top three in palace examination, ranking lower, and was not qualified to apply for imperial academy. His fellow scholar and mentor Huang Renren voluntarily gave up the opportunity to enter the Imperial Academy.
"Biography of Xu Guangqi in Ming Dynasty" begins with 33 words, telling his imperial examination experience, and then says that he "learned astronomy, calendar and firearms from Matteo Ricci, a westerner, and devoted himself to it. Then I read all the books on military training, land reclamation, salt administration and water conservancy. Thus, if I hadn't studied western science with Matteo Ricci, Xu Guangqi was just one of the tens of millions of bureaucrats who owned Ming Yi algebra. However, because he met Matteo Ricci in 1600 and had the opportunity to learn from Matteo Ricci while studying in imperial academy, he had to stand out.
Matteo Ricci 1552 was born in macerata, Italy. In 157 1, he became a trainee monk of the Roman Jesuits. He received extensive training in theology, classical literature and natural science in the church, and learned to draw maps and make various scientific instruments, especially astronomical instruments, in Goa, India.
Matteo Ricci left Rome on May 1577 and arrived in China on February 1583. In August, the "Xianhua Temple" was established in Zhaoqing, Guangdong, and began to preach. But it didn't go well at first. For this reason, Matteo Ricci changed his strategy and decided to adopt the policy of curve missionary. In order to get close to the people of China, Matteo Ricci not only spoke Chinese and wrote Chinese characters, but also tried to make his life China. Dai Bo's dress has also been replaced by a Confucian suit that takes off his coat.
1598 In June, Matteo Ricci went to Beijing to see the emperor, but failed to see him, and returned to Nanjing the following year. Matteo Ricci gained great fame during his stay in Nanjing, especially his unforgettable reciting skills, which left a deep impression on people. When the news spread, it was fascinating. In addition, Matteo Ricci's ingenious social skills, as well as fascinating handicrafts and scientific instruments representing the level of western craftsmanship, attracted high officials, dignitaries and scholars to be happy to associate with him. Matteo Ricci used this to achieve his goal-to promote missionary activities.
It was Matteo Ricci's knowledge and charm that attracted Xu Guangqi. According to Matteo Ricci's diary, it was between July 1597 and May 1600. Xu Guangqi and Matteo Ricci once met, and Matteo Ricci said it was a short meeting. Xu Guangqi mainly asked Matteo Ricci for some Christian teachings, and the two sides did not delve into them. After breaking up with Matteo Ricci, Xu Guangqi spent two or three years studying Christianity and thinking about his own destiny. 1603, Xu Guangqi went to Matteo Ricci again, but Matteo Ricci had already left Nanjing for Beijing. Xu Guangqi met Luo, a missionary who stayed in Ning. After a long talk with him for a few days, he was finally baptized into a Christian.
160 1 year, 1 month, Matteo Ricci was decorated in Beijing again. This time, he succeeded. Matteo Ricci brought a bell and a piano, which need to be repaired frequently. Let him stay in Beijing so that he can often repair it for the emperor. In April of 1604, Xu Guangqi was going to stay in Beijing after he joined the Jinshi. The communication between the two has also increased. Prior to this, Xu Guangqi had a profound understanding of traditional figures in China. After learning western science and technology from Matteo Ricci, he asked Matteo Ricci to cooperate in translating the Elements of Geometry, in order to overcome the defect of traditional mathematics that only said "Fa" but not "Yi", and thought that "it is impossible for him to write this book without translation." Matteo Ricci advised him not to be impulsive because translation is too difficult. Xu Guangqi replied: "Ignorance is the shame of Confucianism."
Reading Selected Works of Geometry Elements 4 Euclid, a great mathematician in ancient Greece, is famous for his masterpiece Geometry Elements. This book is the most famous, complete and widespread mathematical work in the world, and it is also the most valuable work of Euclid. In Elements of Geometry, Euclid systematically summarized the geometric knowledge gained by ancient working people and scholars in practice and thinking. Euclid listed some facts recognized by people as definitions and axioms. Using these definitions and axioms, he studied the properties of various geometric figures by means of formal logic, thus establishing a set of geometric argumentation methods to demonstrate propositions and obtain theorems from axioms and definitions, and forming a strict logical system-geometry. And this book became the cornerstone of European geometry.
For more than two thousand years, The Elements of Geometry has been the main teaching material for studying geometry. Many great scholars, such as Copernicus, Galileo, Descartes and Newton. , studied the elements of geometry, and absorbed rich nutrition from it, thus making many great achievements.
It has been more than two thousand years since Euclid published Elements of Geometry. Despite the rapid development of science and technology, Euclidean geometry has become a good teaching material for cultivating and improving teenagers' logical thinking ability with its vivid intuition and strict logical deduction method. I wonder how many scientists in history have benefited from studying geometry and made great contributions.
When he was a teenager, Newton bought a copy of Geometry in a nightclub near Cambridge University. At first, he thought that the content of the book was not beyond the scope of common sense, so he didn't read it carefully, but he was very interested in Descartes' Coordinate Geometry and read it wholeheartedly. Later, Newton lost the scholarship exam in April. 1664. Dr. Barrow, the examiner at that time, said to him, "Because your basic knowledge of geometry is so poor, no matter how hard you try."
This conversation gave Newton a great shock. Then, Newton studied the Elements of Geometry from beginning to end, which laid a solid mathematical foundation for future scientific work.
However, in the long river of human understanding, no matter how brilliant the predecessors and famous artists are, it is impossible to solve all the problems. Due to the limitation of historical conditions, the "basic" problem of geometry put forward by Euclid in the Elements of Geometry has not been completely solved, and his theoretical system is not perfect. For example, the definition of a straight line is actually an unknown definition to explain another unknown definition, which plays no role in logical reasoning. For another example, Euclid used the concept of "continuity" in logical reasoning, but never mentioned it in the Elements of Geometry.
Reading Selected Works of Geometrical Elements 5 Today I read a book called Geometrical Elements. It is the immortal work of Euclid, an ancient Greek mathematician and philosopher, which combines the achievements and spirit of Greek mathematicians in one book.
The Elements of Geometry contains all the contents of the original volume 13, including 5 axioms, 5 postulates, 23 definitions and 467 propositions, that is, first put forward axioms, postulates and definitions, and then prove them from simple to complex, and on this basis form Euclidean geometry system. Euclid believes that mathematics is a noble world, even as a secular monarch, there is no privilege here. Compared with the decaying matter in time, the world revealed by mathematics is eternal.
The Elements of Geometry is not only a mathematical work, but also full of philosophical spirit, which completes the human understanding of space for the first time. Ancient Greek mathematics was born out of philosophy. It uses all possible descriptions to analyze our universe so that it is not chaotic and inseparable. It is completely different from the secular mathematics in China and ancient Egypt. It establishes a definite system of the material world and the spiritual world, so that people as small as human beings can gain a little confidence from it.
The proposition 1 in this book puts forward how to make equilateral triangles, from which the triangle congruence theorem is produced. That is, angles, sides, angles or sides, angles, sides or sides, sides and sides are equal, and an isosceles triangle-equilateral sides are equilateral; An equilateral is an equilateral. In this way, Euclid put forward his own geometric theory from four parts: point, line, surface and angle. The former proposition paves the way for the latter proposition; The latter proposition is derived from the former, interlocking and very rigorous.
This book is so profound that I can only understand about one tenth, which is very shocking. Euclid deserves to be the father of geometry! He is the most dazzling star in the history of mathematics. I want to learn from him and walk firmly along my own goals.