Euclid (Greek: Ευκλειδης ， From around 330 BC to 275 BC, he was an ancient Greek mathematician known as the "father of geometry". His most famous work "Elements of Geometry" is the foundation of European mathematics, in which he proposed the five postulates.
Euclid's Elements of Geometry is widely regarded as the most successful textbook in history. Euclid also wrote some works on perspective, conic curves, spherical geometry, and number theory.

Background
We know very little about Euclid's background, and his "Elements" is probably a textbook from the University of Alexandria. The University of Alexandria was the last concentration of Greek culture, and because Alexander himself had been to Alexandria, he established the great city of North Africa at that time, located in the Mediterranean Sea. But after his expedition to Asia, we knew he died soon. Afterwards, his great general Ptolemy managed the region of Egypt at that time.
Ptolemy placed great emphasis on learning and established a university. This university is located next to his palace and was the best university in the world at that time, with excellent facilities and many books. Unfortunately, due to religious reasons and numerous other reasons, this school has been completely destroyed now. At that time, Christianity did not like this school and it had already been destroyed. After the Muslims occupied North Africa, they extensively destroyed and burned the books in the library. So now this school doesn't exist at all.
Geometer
Euclid was a famous Greek mathematician and founder of Euclidean geometry. Euclid was born in Athens, which was the center of ancient Greek civilization at that time. The rich cultural atmosphere deeply infected Euclid, and when he was still a teenager, he couldn't wait to enter Plato Academy to study.
One day, a group of young people arrived at the Platonic Academy located in the shade of trees on the outskirts of Athens. The gate of the school was tightly closed, with a wooden sign hanging on it that read: "Those who do not understand geometry are not allowed to enter!" This was a rule personally established by Plato in the past to let students know his importance to mathematics, but it confused the young people who came to seek advice. Someone is thinking, it's because I don't understand mathematics that I came here to seek advice. If I understand, what else would I do here? As people looked at each other, unsure whether to move in or out, Euclid walked out of the crowd. He straightened his clothes, looked at the sign, and decisively pushed open the school gate, walking in without looking back.

Write a masterpiece
The earliest geometry emerged in ancient Egypt in the 7th century BC, and later spread to the capital of ancient Greece through the ancient Greeks, laying the foundation through the Pythagorean school system. Before Euclid, people had already accumulated a lot of knowledge in geometry, but this knowledge had a major drawback and deficiency, which was the lack of systematicity. Most of the knowledge is fragmented and fragmented, with no strong connection between axioms and proofs, let alone strict logical reasoning and explanation of formulas and theorems.
Therefore, with the prosperity and development of the social economy, especially with the development of agriculture, forestry, and animal husbandry, as well as the increase in land development and utilization, organizing and systematizing these geometric knowledge into a complete set of knowledge systems that can be logically explained and interconnected, has become an urgent trend in scientific progress. Euclid, through his early and thorough study of Plato's mathematical ideas, especially the theoretical system of geometry, has keenly sensed the development trend of geometric theory.
He made up his mind to complete this work in his lifetime and become the first person in geometry. In order to accomplish this important task, Euclid spared no effort and traveled a long distance from the ancient city of Athens on the Aegean coast to the new port of Egypt in the Nile River basin - Alexandria, in order to achieve his original intention in this emerging and culturally rich foreign city. Throughout countless days and nights here, he collected past mathematical monographs and manuscripts, sought advice from scholars, and attempted to write books and explain his understanding of geometry, even if it was only a superficial understanding. After Euclid's selfless work, a fruitful harvest was finally produced in 300 BC, which was the final finalized "Elements of Geometry" after several revisions. This is a masterpiece that has been passed down for generations. With it, geometry not only achieved systematization and organization for the first time, but also gave birth to a new research field - Euclidean geometry, abbreviated as Euclidean geometry. Until today, the geometry he created was still a compulsory course in schools around the world, and his laws, theories, and formula applications are present in every subject from elementary to middle school, university, and modern higher education.

There is no shortcut
In the "Outline of the Development of Geometry" by the late mentor of the Platonic school, Proclus (around 410 AD to 485 AD), there is a story about mathematics gradually becoming a fashionable topic in people's lives under the promotion of Euclid (which is completely opposite to today's society), to the extent that King Ptolemy I of Alexandria wanted to catch up with this trend and learn some geometry at that time.
Although this king was knowledgeable and knowledgeable, Euclidean geometry made it difficult for him to learn. So he asked Euclid, "Is there any shortcut to learning geometry?" Euclid smiled and said, "I'm sorry, Your Majesty! Learning mathematics is like learning all sciences, there is no shortcut. Learning mathematics requires everyone to think independently, just like planting crops. Without cultivation, there will be no harvest. In this regard, the king and the ordinary people are the same." From then on, "In geometry, there is no great road specially laid for kings." This sentence has become a timeless learning motto.

biomass pyramid
At that time, people built tall pyramids, but no one knew how high the pyramids were. Someone said, "To measure the height of a pyramid, it's even harder than climbing to the sky!" This statement reached Euclid's ears. He smiled and told others, "What's so difficult about this? When your shadow is the same length as your body, measure how long the shadow of the pyramid is, and the length will be equal to the height of the pyramid!"

No benefits
More and more people are coming to study geometry as a teacher in Euclid. Some people come to join in the fun, and when they see others learning geometry, they also learn geometry. Stobez recounted another story. A student once asked Euclid, "Teacher, what benefits will learning geometry bring me?" Euclid pondered for a moment and asked his servant to bring some money to the student. Euclid said: Give him three coins (about 500) because he wants to gain practical benefits in his studies.

Perfect number
In addition, Euclid also explored perfect numbers in "Elements of Geometry", discovering the first four perfect numbers through the expression of 2 ^ (n) · (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 perfect 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, while the necessity is proved by Euler.
Among them, 2 ⁽ⁿ⁾⁻ ¹ It is a prime number, and the 6 and 28 above correspond to the case of n=2 and 3. We just need to find a shape like 2 ⁽ⁿ⁾⁻ ¹ A prime number (also known as a Mason prime) is known as an even perfect number. In the era of manual calculation, Mason prime numbers made it more convenient for people to calculate perfect numbers, and in the era of computers, they were widely and deeply applied. The CPU of computers can more conveniently calculate various numbers.
Although no odd perfect numbers have been found, contemporary mathematician Austin Orr proved that if there is an odd perfect number, its form must be either 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:

Euclidean algorithmGeometric Elements
The Elements of Geometry is an immortal work that combines the ideas of predecessors and Euclid's personal creativity. This book has basically covered the mathematical development history of geometry from the 7th century BC to ancient Greece, all the way to the 4th century BC - the period of Euclid's life - for a total of over 400 years.
It not only preserves many early geometric theories of ancient Greece, but also promotes these ancient mathematical ideas through Euclid's pioneering systematic organization and complete exposition. It pioneered the study of classical number theory and, based on a series of axioms, definitions, and postulates, established the Euclidean geometry system, becoming the earliest model of mathematical deduction systems established using axiomatization methods.
The whole book is divided into 13 volumes. The book contains 5 axioms, 5 postulates, 23 definitions, and 467 propositions.
In each volume of content, Euclid adopts a completely different narrative approach from his predecessors, which first proposes axioms, postulates, and definitions, and then proves them from simple to complex. This makes the discussion throughout the book more concise and clear.
And in the content arrangement of the entire book, his unique and ingenious arrangement is also implemented. It goes from shallow to deep, from simple to complex, and successively discusses topics such as straight edges, circles, proportion theory, similarity forms, numbers, solid geometry, and exhaustion method. The discussion about the exhaustion method has become the source of modern calculus thought.
According to the system of Euclidean geometry, all theorems are derived from certain fundamental propositions, namely axioms, that are definite and do not require proof to be true. In this deductive reasoning, each proof of a theorem must be based on either axioms or previously proven theorems, and a conclusion must be drawn. Has had a profound impact on future generations.

Character works
His most famous work "Elements of Geometry" is the foundation of European mathematics, summarizing the five postulates of plane geometry, and is widely regarded as the most successful textbook in history. Euclid also wrote some works on perspective, conic curves, spherical geometry, and number theory. Euclid used the method of axiomatization. This method later became a model for establishing any knowledge system, and for almost two thousand years, it was regarded as an example of rigorous thinking that must be followed.
In addition to "Elements of Geometry", he has many other works, but unfortunately most of them have been lost. Euclid has five other works that have been passed down to this day. They, like the Elements of Geometry, both contain definitions and proofs.
"The Known Numbers" is the only Greek purely geometric work that has been preserved except for "The Original," with a format similar to the first six volumes of "The Original," including 94 propositions. If certain elements in the graph are known, then other elements can also be determined.
On divisions of figures, existing Latin and Arabic texts, discuss the use of straight lines to divide known shapes into equal or proportional parts, similar to the works of Heron of Alexandria.
Catoptics discusses the mathematical theory of reflected light, particularly images formed on flat and concave mirrors. But some people question whether this book truly came from Euclid, and its author may be Theon of Alexandria.
Phenomena is a paper 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 on geometric optics, with existing Greek texts. This book mainly studies perspective problems, describing the incidence angle and reflection angle of light. Believing that vision is the result of the eyes emitting light to reach objects. Some works have not been determined whether they belong to Euclid and have been lost.

Euclid was one of the most famous and influential mathematicians in ancient Greece. Euclid's Elements of Geometry had a great impact on the future development of geometry, mathematics, and science, as well as the entire way of thinking of Westerners.
The Elements of Geometry was the pinnacle of the development of ancient Greek mathematics. Euclid organized the rich achievements accumulated in Greek geometry since the 7th century BC into a rigorous logical system of operations, making geometry an independent and deductive science.
The Euclidean algorithm, also known as the convolutional division, is used to calculate the maximum common divisor of two integers a and b.