Euclid (English: Euclid; Greek: ε υ κ λ ε ι δ η _ (about 330 BC-275 BC), an ancient Greek mathematician, was called "the father of geometry". His most famous book, The Elements of Geometry, is the foundation of European mathematics, and puts forward five postulates, Euclidean Geometry, which is widely regarded as the most successful textbook in history. Euclid also wrote some works about perspective, conic curve, spherical geometry and number theory.

Chinese name: Euclid

Mbth: ε υ κ λ ε ι δ η _

Alias: Euclid

Nationality: Ancient Greece

Place of birth: Athens

Date of birth: about 330 BC

Date of death: 275 BC

Occupation: Mathematician

Belief: polytheism

Main achievements: Mathematical masterpiece "The Elements of Geometry"

Euclid algorithm

perfect number

Masterpiece: The Elements of Geometry

Language: Ancient Greek

Character story

Someone's (unfortunate) fate

We know little about Euclid's life experience. His Elements of Geometry is probably a textbook of Alexandria University. The University of Alexandria is the last place where Greek culture is concentrated. Because Alexander himself has been to Alexandria, he established a big city in North Africa at that time, near the Mediterranean Sea. But after his expedition to Asia, we know that he died soon. Later, his general Ptolemy managed the area of Egypt at that time.

Ptolemy attached great importance to learning and established a university. The university is next to his palace. It was the best university in the world at that time. It is well-equipped and has many books. Unfortunately, due to religious reasons and many reasons, this school has now been completely destroyed. At that time, Christianity didn't like this school, so it was ruined. After Muslims occupied North Africa, they destroyed and burned books in libraries on a large scale. So now this school doesn't exist at all.

Geometrician

Euclid was a famous mathematician in ancient Greece and the pioneer of Euclid geometry. Euclid was born in Athens, the center of ancient Greek civilization. The rich cultural atmosphere deeply infected Euclid. When he was a teenager, he couldn't wait to enter Plato College.

One day, a group of young people came to Plato's Academy in the shade outside Athens. I saw that the gate of the academy was closed and there was a wooden sign hanging at the door, which read: "Those who don't know geometry are not allowed to enter!" This is a rule set by Plato himself. In order to let the students know that he attaches importance to mathematics, it confuses the young people who come to ask for advice. Some people are thinking that I want to come here for advice because I don't know math. If I know, why am I here? Just when people looked at each other and didn't know whether to enter or retreat, Euclid came out of the crowd. He adjusted his clothes, glanced at the sign, and then decisively pushed open the door of the academy and went in without looking back.

Write a masterpiece

The earliest geometry rose in ancient Egypt in the 7th century BC, and was later spread to the ancient Greek capital by the ancient Greeks and others, and the Pythagorean school system laid the foundation stone. Before Euclid, people had accumulated a lot of knowledge about geometry. However, there is a great shortcoming and deficiency in this knowledge, that is, lack of systematicness. Most of them are fragmentary knowledge, and there is no strong connection between axioms and proofs, let alone strict logical demonstration and explanation of formulas and theorems.

Therefore, with the prosperity and development of social economy, especially the development of agriculture, forestry and animal husbandry, and the increase of land development and utilization, it is urgent to organize and systematize these geometric knowledge and form a set of self-justified and clear-cut knowledge system, which has become the general trend of scientific progress. Euclid has been keenly aware of the development trend of geometric theory through his early systematic and in-depth study of Plato's mathematical thought, especially geometric theory.

He made up his mind to finish this work in his lifetime and become the first person in geometry. In order to accomplish this task, Euclid set out from the ancient city of Athens on the Aegean Sea and went to Alexandria, a new port in Egypt in the Nile Valley, to realize his original intention in this brand-new but culturally rich foreign city. During countless days and nights here, he collected previous mathematical monographs and manuscripts, consulted relevant scholars, and tried to write a book to clarify his understanding of geometry, even if it was superficial. After Euclid's selfless labor, he finally produced rich fruits in 300 BC. This is the book Geometry, which was finalized after several drafts. This is a masterpiece handed down from generation to generation. With it, geometry was not only systematized and organized for the first time, but also gave birth to a brand-new research field-Euclidean geometry. Until today, his geometry is still a compulsory course in schools all over the world, and his laws, theories and formulas are being applied in all disciplines from primary school to junior high school, universities and modern higher education.

There is no shortcut.

In the Outline of Geometry Development written by Proklose (about 465,438+00 ~ 485), the late mentor of Plato School, there is a story that, under the impetus of Euclid (contrary to today's society), mathematics gradually became a fashionable topic in people's lives, so that Ptolemy I Soter, king of Alexandria at that time, wanted to catch up with this fashion and learn some geometry.

Although the king is well-informed, Euclidean geometry is 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, like learning all science subjects, has no shortcut. When learning mathematics, everyone should think independently, just like planting crops. If you don't work hard, you will get nothing. In this respect, kings are the same as ordinary people. " Since then, "in geometry, there is no road paved for kings." This sentence has become an eternal learning motto.

Quantitative pyramid

There is another story. At that time, people built tall pyramids, but no one knew how high they were. Someone said, "It is more difficult to measure the height of the pyramid than to climb to the sky!" " "This word reached the ears of Euclid. He smiled and told others, "What's so hard about this? When your shadow is as long as your body, measure how long the shadow of the pyramid is, and the length is equal to the height of the pyramid! "

No benefit

More and more people come to study geometry with Euclid as their teacher. Some people come to join in the fun. They see others learning geometry, and they learn geometry themselves. Stobeus (about 500) tells another story. A student once asked Euclid, "Teacher, what benefits will I get from studying geometry?" On reflection, Euclid asked the servant to give the students some money. Euclid said: Give him three coins because he wants to get real benefits from his study.

Personality achievement

perfect number

In addition, Euclid also explored the perfect number in the Elements of 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).

Where 2 (n)- 1 is a prime number, and the above 6 and 28 correspond to the case where n=2 and 3. As long as you find a prime number (mersenne prime) with the shape of 2 (n)- 1, you will know an even perfect number. In the era of hand calculation, mersenne prime can make people calculate the perfect number more conveniently, and it has been widely used in the computer age, and the CPU of the computer can calculate various numbers more conveniently.

Although the odd perfect number has not been found, the contemporary mathematician Austin Orr proved that if there is an odd perfect number, its form must be 12p+ 1 or 36p+9, where p is a prime number. There is no odd perfect number for natural numbers below 10 300.

The first five perfect numbers are:

six

28

496

8 128

33550336

Euclid algorithm

Euclid algorithm, also known as division by turns, is used to calculate the greatest common divisor of two integers A and B. ..

Geometry originally

The Elements of Geometry is an immortal work that combines the thoughts of predecessors and Euclid's personal creativity. This book has basically covered the history of mathematical development of geometry from the 7th century BC to ancient Greece, to the 4th century BC, when Euclid lived.

It not only preserved many early geometric theories of ancient Greece, but also carried forward these ancient mathematical ideas through Euclid's pioneering systematic arrangement and complete exposition. 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 adopts a completely different narrative method from the predecessors, that is, first put forward axioms, postulates and definitions, and then prove them from simple to complex. This makes the discussion of the whole book more compact and vivid.

He also made his own original arrangement in the content arrangement of the whole book. From shallow to deep, from simple to complex, this paper discusses straight edge, circle, proportion theory, similarity, number, solid geometry and exhaustive method. The discussion on exhaustive method has become the source of modern calculus thought.

According to the system of Euclidean geometry, all theorems are derived from some basic propositions that are true without proof, that is, axioms. In this deductive reasoning, every proof of a theorem must be based on axioms or theorems that have been proved before, and finally a conclusion is drawn. It has had a far-reaching impact on later generations.

Character works

His most famous book, The Elements of Geometry, is the foundation of European mathematics, which summarizes five postulates of plane geometry and is widely regarded as the most successful textbook in history. Euclid also wrote some works about perspective, conic curve, spherical geometry and number theory. Euclid used the axiomatic method. This method later became a model of establishing any knowledge system, and in almost two thousand years, it was regarded as a model of rigorous thinking that must be followed.

Besides the Elements of Geometry, he has many other works, but most of them have been lost. Five other works of Euclid have survived to this day. Like geometric elements, they all contain definitions and proofs.

The Materials is the only Greek pure geometry book except The Original, and its style is similar to the first six volumes of The Original, including 94 propositions. It should be pointed out that if some elements in the diagram are known, other elements can also be determined.

The existing Latin and Arabic texts of Division of Circle discuss that known figures are divided into equal parts or proportional parts by straight lines, which is similar to HeronofAlexandria's works.

Reflectometry discusses the mathematical theory of reflected light, especially images on plane and concave mirror. However, some people question whether this book was really written by Euclid, and the author may be TheonofAlexandria.

Phenomenon is a paper on spherical astronomy, and the existing Greek text. This book is similar to "OntheMovingSphere" written by Otto Ricus of Lecosse.

Optics is one of the early works of geometric optics, with Greek text. This book mainly studies perspective and describes the incident angle and reflection angle of light. It is believed that vision is the result of the light from the eyes reaching the object. There are still some works that are not sure whether they belong to Euclid or not, and have been lost.

Personality assessment

Euclid was one of the most famous and influential mathematicians in ancient Greece. Euclid's Elements of Geometry has a great influence on the later development of geometry, mathematics and science, and on the whole thinking method of westerners. The Elements of Geometry is the pinnacle of the development of ancient Greek mathematics. Euclid arranged the rich achievements accumulated in Greek geometry since the seventh century BC in strict logical system operation, making geometry an independent and deductive science.