Euclid (Greek: Ευκλειδης ， About 330 BC - 275 BC), an ancient Greek mathematician, known as the "father of geometry". His most famous book "The Original Geometry" is the basis of European mathematics, in which he proposed five postulates.
Euclid's Original Geometry is widely regarded as the most successful textbook in history. Euclid also wrote some works on perspective, conics, spherical geometry and number theory.

Experience
We know very little about Euclid's life experience. His "Original Geometry" is probably a textbook of Alexander University. The University of Alexandria was the last place where Greek culture was concentrated. Because Alexander himself had been to Alexandria, he built a big city in North Africa at that time, which was close to the Mediterranean Sea. But after his expedition to Asia, we know that he died soon. Later, his general Ptolemy managed the Egyptian region at that time.
Ptolemy attached great importance to learning and established a university. This university is next to his royal palace. It was the best university in the world at that time, with excellent facilities and many books. Unfortunately, due to religious reasons and many other reasons, the school has been completely destroyed. At that time, Christianity did not like the school and it was destroyed. After the Muslim occupation of North Africa, they destroyed and burned the books in the library on a large scale. So now this school doesn't exist at all.
Geometer
Euclid was a famous mathematician and founder of Euclidean geometry in ancient Greece. Euclid was born in Athens, which was the center of ancient Greek civilization at that time. Euclid was deeply affected by the rich cultural atmosphere. When he was a teenager, he couldn't wait to enter Plato School.
One day, a group of young people came to the Plato School Park, which is located in the shade outside Athens. I saw that the gate of the school park was closed, and there was a wooden sign hanging on the door, which said, "Those who do not know geometry, are not allowed to enter!" This was the rule set by Plato in order to let the students know that he attached importance to mathematics, but it confused the young people who came to ask for advice. Some people are thinking that it is because I don't understand mathematics that I want to come here for advice. If I understand, what else do I do here? While people were looking at each other and wondering whether to go in or out, Euclid came out of the crowd. He adjusted his clothes, looked at the sign, and then decisively opened the gate of the school park, and walked in without turning back.

Compile great works
Geometry
Geometry
The earliest geometry rose in ancient Egypt in the 7th century BC, and then spread to the capital of ancient Greece by the ancient Greeks, and laid the foundation by the Pythagorean school system. Before Euclid, people had accumulated a lot of geometry knowledge, but there was a big shortcoming and deficiency in these knowledge, that is, lack of systematicness. Most of them are fragmentary and fragmentary knowledge. There is no strong connection between axioms and axioms, between proofs and proofs, let alone strict logical argumentation and explanation of formulas and theorems.
Therefore, with the prosperity and development of social economy, especially with the development of agriculture, forestry and animal husbandry, and the increase of land development and utilization, the systematization and systematization of these geometric knowledge into a complete set of knowledge system that can be justified and connected back and forth has become a major trend of scientific progress. Euclid has been keenly aware of the development trend of geometric theory through his early systematic and thorough study of Plato's mathematical thought, especially the geometric theory.
He made up his mind to finish the work in his lifetime and become the first person in geometry. In order to accomplish this important task, Euclid made a long journey from the ancient city of Athens on the Aegean coast to Alexandria, the new port of Egypt in the Nile basin, in order to realize his original intention in this new and culturally rich foreign city. During the countless days and nights here, he collected the previous mathematical monographs and manuscripts, consulted the relevant scholars, and tried to write books and explain his understanding of geometry, even superficial. After Euclid's selfless work, it finally produced fruitful results in 300 BC. This is the Geometry Original, which was finalized after several drafts. This is a masterpiece handed down from generation to generation. With it, geometry has not only realized systematization and systematization for the first time, but also bred a new research field - Euclidean geometry, or Euclidean geometry for short. Until today, the geometry he created is still a compulsory course in schools around the world. From primary school to junior high school, university, and modern higher disciplines, there are laws, theories and formula applications he created.

In the "Outline of Geometry Development" of Proclos, the late mentor of the Platonic School (about 410~485), there is a story that mathematics, driven by Euclid, has gradually become a fashionable topic in people's life (this is diametrically opposed to today's society), so that at that time, King Ptolemy I of Alexandria wanted to catch up with this trend and learn geometry.
Although the king was well informed, Euclidean geometry made him study hard. So he asked Euclid, "Is there any shortcut to learn geometry?" Euclid laughed and said, "Sorry, your majesty! There is no shortcut to learn mathematics, just like learning all science. To learn mathematics, everyone has to think independently, just like planting crops. There will be no harvest without farming. In this respect, the king and ordinary people are the same." From then on, "In geometry, there is no road specially paved for the king." This sentence has become a learning maxim that has been handed down for thousands of years.
biomass pyramid
Pyramid
Pyramid
At that time, people built tall pyramids, but no one knows how high the pyramids are. Someone said, "It is more difficult to measure the height of the pyramid than to climb to the sky!" This word spread to Euclid. He smiled and told others, "What's the difficulty? When your shadow is as long as your body, you should measure how long the shadow of the pyramid is, and the length is equal to the height of the pyramid!"
No benefits
There are more and more people who come to learn geometry. Some people come to make fun of it. When they see others learning geometry, they also learn geometry. Stobez recounted another story. A student once asked Euclid, "Teacher, what benefits will I get from studying geometry?" Euclid thought for a while and asked the servant to bring some money to the student. Euclid said: Give him three coins (about 500), because he wants to gain real benefits in his study.

Perfect number
In addition, Euclid also explored the perfect number in the "Original Geometry". He found the first four perfect numbers through the expression of 2 ^ (n-1) · (2 ^ n-1).
When n=2: 2 ^ 1 (2 ^ 2-1)=6 when n=3: 2 ^ 2 (2 ^ 3-1)=28 when n=5: 2 ^ 4 (2 ^ 5-1)=496 when n=7: 2 ^ 6 (2 ^ 7-1)=8128 an even number is a complete number if and only if it has the following form: 2 ^ (n-1) (2 ^ n-1) The sufficiency of this fact is proved by Euclid, and the necessity is proved by Euler.
Among them, 2 ⁽ⁿ⁾⁻ ¹ Is a prime number. The above 6 and 28 correspond to the case of n=2 and 3. We just need to find a shape like 2 ⁽ ⁿ ⁾ ⁻ ¹ The prime number (that is, the Mason prime number), also known as an even complete number. In the era of manual calculation, Mason prime numbers can make people more convenient to calculate complete numbers. In the era of computer, it has been widely and deeply used. The CPU of computer can calculate various numbers more conveniently.
Although no odd perfect number has been found, the contemporary mathematician Austin Ouer proved that if there is an odd perfect number, its form must be 12p+1 or 36p+9, where p is a prime number. At 10 ³ Odd perfect numbers do not exist in natural numbers below degrees.
The first five perfect numbers are:
six
twenty-eight
four hundred and ninety-six
eight thousand one hundred and twenty-eight
thirty-three million five hundred and fifty thousand three hundred and thirty-six
Euclidean algorithm
Euclidean algorithm, also known as rolling division, is used to calculate the maximum common divisor of two integers a and b. [1]
Geometric origin
The Original Geometry is an immortal work that combines the ideas of predecessors and Euclid's personal creativity. This book has basically covered more than 400 years of mathematical development history of geometry from the 7th century BC to ancient Greece, to the 4th century BC - the life of Euclid.
It not only preserved many early geometric theories of ancient Greece, but also carried forward these ancient mathematical ideas through the pioneering systematic arrangement and complete exposition of Euclid. It initiated the study of classical number theory, founded Euclidean geometry system on the basis of a series of axioms, definitions and postulates, and became the earliest model of mathematical deduction system established by axiomatic method.
The book is divided into 13 volumes. The book contains five "axioms", five "postulates", 23 definitions and 467 propositions.
In each volume, Euclid adopted a completely different way of narration from his predecessors, that is, first put forward axioms, postulates and definitions, and then prove them from simple to complex. This makes the whole book more compact and lively.
In the content arrangement of the whole book, he also carried out this ingenious arrangement. From shallow to deep, from simple to complex, it has successively discussed the contents of straight side, circle, proportion theory, similar shape, number, solid geometry and exhaustion method. Among them, the discussion of exhaustion method became the source of modern calculus thought.
According to the system of Euclidean geometry, all theorems are derived from certain basic propositions, namely axioms, which are absolutely true without proof. In this kind of deductive reasoning, each proof of a theorem must be based on either axioms or a theorem that has been proved before, and finally a conclusion is made. It has had a profound impact on later generations.
Character works
His most famous book, The Original Geometry, is the basis of European mathematics, summarizing the five postulates of plane geometry, and is widely considered as the most successful textbook in history. Euclid also wrote some works on perspective, conics, spherical geometry and number theory. Euclid used the axiomatic method. This method later became a model for the establishment of any knowledge system. For almost two thousand years, it was regarded as an example of rigorous thinking that must be followed.
In addition to the "Original Geometry", he has many works, but most of them are lost. Euclid has five other works that have been handed down to this day. They contain definitions and proofs, just like the original geometry.
Data is the only Greek purely geometric work that has been preserved except the original. Its style is similar to the first six volumes of the original, including 94 propositions. It is pointed out that if some elements in the graph are known, other elements can also be determined.
On divisions of figures, the existing Latin text and Arabic text, discusses the use of straight lines to divide known figures into equal or proportional parts, and the content is similar to that of Heron of Alexandria.
"Reflective Optics" discusses the mathematical theory of reflected light, especially the image formed on the plane and concave mirror. However, some people question whether this book is really written by Euclid. Its author may be Theon of Alexandria.
Phenomena is a treatise on spherical astronomy, with existing Greek texts. This book is similar to On the Moving Sphere written by Autolycus of Pitane.
Optics is one of the early works of geometric optics, existing Greek text. This book mainly studies perspective problems, and describes the incidence angle and reflection angle of light. It is believed that vision is the result of the light emitted by the eyes reaching the object. There are still some works that have not been determined whether they belong to Euclid and have been lost.