We invite you to meet such a great mathematician as Euclid. Biography, a summary of his main work and some interesting facts about this scientist are presented in our article. Euclid (years of life - 365-300 BC) is a mathematician belonging to the Hellenic era. He worked in Alexandria under Ptolemy I Soter. There are two main versions of where he was born. According to the first - in Athens, according to the second - in Tire (Syria).
Euclid's biography: interesting facts
Not much is known about the life of this scientist . There is a message belonging to Papp of Alexandria. This man was a mathematician who lived in the 2nd half of the 3rd century AD. He noted that the scientist we were interested in was kind and gentle with all those who could at least somehow contribute to the development of certain mathematical sciences.
There is also a legend that Archimedes reported. Her main character is Euclid. A short biography for children usually includes this legend, since it is very curious and can cause interest in this mathematician among young readers. It says that King Ptolemy wanted to study geometry. However, it turned out that this is not easy. Then the king called the scientist Euclid and asked him if there was any easy way to comprehend this science. But Euclid replied that there was no royal road to geometry. So this expression, which has become winged, has come down to us in the form of a legend.
At the beginning of the 3rd century BC e. founded the Alexandria Museum and the Alexandria Library Euclid. A brief biography and its discoveries are associated with these two institutions, which were also training centers.
Euclid - a student of Plato
This scientist went through the Academy, founded by Plato (his portrait is presented below). He learned the main philosophical idea of this thinker, which was that there is an independent world of ideas. It is safe to say that Euclid, whose biography was stingy with details, was a Platonist in philosophy. Such an attitude strengthened the scientist in the understanding that everything that was created and set forth by him in his "Principles" has an eternal existence.
The thinker of interest to us was born 205 years later than Pythagoras, 63 years - Plato, 33 - Eudoxus, 19 - Aristotle. He became acquainted with their philosophical and mathematical works, either independently or through intermediaries.
The connection of the "Beginnings" of Euclid with the works of other scientists
Proclus Diadoch, a neo-Platonic philosopher (412-485 years of life), author of comments on the Beginnings, suggested that this essay reflects the cosmology of Plato and the Pythagorean Doctrine ... In his work, Euclid presented the theory of the golden section (books 2, 6 and 13) and regular polyhedra (book 13). Being an adherent of Platonism, the scientist understood that his “Beginnings” contribute to the cosmology of Plato and to the ideas developed by his predecessors about the numerical harmony that characterizes the universe.
Not one Proclus Diadoch appreciated Platonic solids and the golden ratio. Johannes Kepler (years of life - 1571-1630) was also interested in them. This German astronomer noted that in geometry there are 2 treasures - this is the golden ratio (dividing a segment in the middle and extreme ratio) and the Pythagorean theorem. He compared the value of the last of them with gold, and the first with a gem. Johannes Kepler used Platonic solids to create his cosmological hypothesis.
Meaning "Started"
The book "Beginnings" is the main work that Euclid created. The biography of this scientist, of course, is noted by other works, which we will discuss at the end of the article. It should be noted that the works with the name "Beginnings", which set forth all the most important facts of theoretical arithmetic and geometry, were also compiled by his predecessors. One of them is Hippocrates of Chios, a mathematician who lived in the 5th century BC. e. Feudius (2nd half of the 4th century BC) and Leont (4th century BC) also wrote books with that name. However, with the advent of the Euclidean "Beginnings" all these works were supplanted from everyday life. Euclid's book has been a basic textbook on geometry for over 2 thousand years. The scientist, creating his work, used many of the achievements of his predecessors. Euclid processed the available information and brought the material together.
In his book, the author summed up the development of mathematics in ancient Greece and created a solid foundation for further discoveries. This is the significance of the main work of Euclid for world philosophy, mathematics, and science as a whole. It would be wrong to believe that it consists in strengthening the mysticism of Plato and Pythagoras in their pseudo-universe.
Many scholars have appreciated the "Beginnings" of Euclid, including Albert Einstein. He noted that this is an amazing work that gave the human mind the self-confidence necessary for further activities. Einstein said that the man who did not admire this creation in his youth was not born for theoretical research.
Axiomatic method
It should be noted separately the importance of the work of the scientist that interests us in a brilliant demonstration of the axiomatic method in his "Principles". This method in modern mathematics is the most serious of those used to substantiate theories. In mechanics, it also finds wide application. The great scientist Newton built the "Beginnings of Natural Philosophy" on the model of the work that Euclid created.
The biography of the author of interest to us continues with a description of the main points of his main work.
Basic Provisions
The book "Beginnings" systematically expounds Euclidean geometry. Its coordinate system is based on such concepts as a plane, line, point, motion. The relationships that are used in it are as follows: “the point is located on a straight line lying on the plane” and “the point is located between two other points”.
The system of positions of Euclidean geometry presented in the modern presentation is usually divided into 5 groups of axioms: Euclidean movement, order, continuity, combination and parallelism.
In thirteen books "Beginnings" the scientist presented arithmetic, stereometry, planimetry, and Eudox relations. It should be noted that the presentation in this work is strictly deductive. Each book of Euclid begins with definitions, and in the first of them axioms and postulates follow. Next come sentences that are divided into problems (where it is necessary to build something) and theorems (where it is necessary to prove something).
Lack of math Euclid
The main disadvantage is that the axiomatics of this scientist is devoid of completeness. There are no axioms of motion, continuity and order. Therefore, the scientist often had to trust the eye, resort to intuition. Books 14th and 15th are later additions to labor, the author of which is Euclid. His biography is only very brief, so it is impossible to say for sure whether the first 13 books were created by one person or whether they are the result of the collective work of the school, which was led by a scientist.
Further development of science
The appearance of Euclidean geometry is associated with the emergence of visual representations of the world around us (rays of light, stretched threads as an illustration of straight lines, etc.). Further they deepened, due to which a more abstract understanding of such a science as geometry arose. N. I. Lobachevsky (years of life - 1792-1856) is a Russian mathematician who made an important discovery. He noted that there is a geometry that is different from Euclidean. This has changed the way scientists think about space. It turned out that they are by no means a priori. In other words, the geometry set forth in the "Beginnings" of Euclid cannot be considered the only one describing the properties of the space surrounding us. The development of natural science (primarily astronomy and physics) has shown that it describes its structure only with a certain accuracy. In addition, it cannot be applied to the entire space as a whole. Euclidean geometry is the first approximation to understanding and describing its structure.
By the way, the fate of Lobachevsky was tragic. He was not accepted in the scientific world for his bold thoughts. However, the struggle of this scientist was not in vain. The triumph of Lobachevsky's ideas was ensured by Gauss, whose correspondence was published in 1860. Among the letters were enthusiastic reviews of the scientist about the geometry of Lobachevsky.
Other works of Euclid
Very much interest in our time is the biography of Euclid as a scientist. In mathematics, he made important discoveries. This is confirmed by the fact that since 1482, the book "Beginnings" has already survived more than five hundred editions in various languages of the world. However, the biography of the mathematician Euclid is marked by the creation of not only this book. He owns a number of works on optics, astronomy, logic, and music. One of them is the book "Data", which describes the conditions that make it possible to consider this or that mathematical maximum image as "data". Another Euclidean work is a book on optics, which contains information about the future. The scientist of interest to us also wrote an essay on catoptrics (he outlined in this work the theory of distortions arising in mirrors). The book of Euclid is also known under the name "Division of figures". Unfortunately, the work on mathematics On False Conclusions has not been preserved.
So, you met such a great scientist as Euclid. A brief biography of him, we hope, has been useful to you.