We invite you to meet such a great mathematician as Euclid. A 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) - 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 Tyre (Syria).
Euclid's biography: interesting facts
Not much is known about this scientist's life. There is a message belonging to Pappus of Alexandria. This man was a mathematician who lived in the 2nd half of the 3rd century AD. He noted that the scientist of interest to us was kind and gentle with all those who could somehow contribute to the development of certain mathematical sciences.
There is also a legend told by Archimedes. Its main character is Euclid. A short biography for children usually includes this legend, as it is very curious and can arouse interest in this mathematician among young readers. It says that King Ptolemy wanted to study geometry. Howeverit turned out that this is not easy to do. Then the king called the learned 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 Museum of Alexandria and the Library of Alexandria Euclid. A brief biography and his discoveries are associated with these two institutions, which were also educational centers.
Euclid - a student of Plato
This scientist went through the Academy founded by Plato (his portrait is shown 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 is stingy with details, was a Platonist in philosophy. Such an attitude strengthened the scientist in the understanding that everything that he created and set forth in his "Principles" has an eternal existence.
The thinker we are interested in was born 205 years later than Pythagoras, 63 years later Plato, 33 years later Eudoxus, 19 years later Aristotle. He got acquainted with their philosophical and mathematical works either independently or through intermediaries.
Relationship of Euclid's "Beginnings" with the works of other scientists
Proclus Diadochus, Neoplatonist philosopher (years of life - 412-485), author of comments on the "Principles", suggested that this work reflectsPlato's cosmology and "Pythagorean doctrine…". In his work, Euclid outlined 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 Plato's cosmology and to the ideas developed by his predecessors about the numerical harmony that characterizes the universe.
Proclus Diadoch was not alone in appreciating the Platonic solids and the golden ratio. Johannes Kepler (years of life - 1571-1630) was also interested in them. This German astronomer noted that there are 2 treasures in geometry - this is the golden ratio (division of a segment in the middle and extreme ratio) and the Pythagorean theorem. The value of the last of them he compared with gold, and the first - with a precious stone. Johannes Kepler used Platonic solids in creating his cosmological hypothesis.
Meaning "Started"
The book "Beginnings" is the main work that Euclid created. The biography of this scientist, of course, is marked by other works, which we will talk about at the end of the article. It should be noted that the works with the title "Beginnings", which set out all the most important facts of theoretical arithmetic and geometry, were compiled by his predecessors. One of them is Hippocrates of Chios, a mathematician who lived in the 5th century BC. e. Theudius (2nd half of the 4th century BC) and Leontes (4th century BC) also wrote books with this title. However, with the advent of Euclidean "Beginnings" all these works were forced out of use. Euclid's book was the baseteaching aid in geometry for over 2,000 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 Euclid's main work for world philosophy, mathematics and all science in general. It would be wrong to believe that it consists in strengthening the mysticism of Plato and Pythagoras in their pseudo-universe.
Many scientists have appreciated Euclid's Elements, 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 person who did not admire this creation in his youth was not born for theoretical research.
Axiomatic method
We should separately note the importance of the work of the scientist of interest to us in the 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 "Principles 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 provisions of his main work.
Basics of "Started"
In the book"Beginnings" systematically expounds Euclidean geometry. Its coordinate system is based on concepts such as plane, line, point, movement. The relations used in it are: "a point is located on a straight line lying on a plane" and "a point is located between two other points".
The system of provisions of Euclidean geometry, presented in the modern presentation, is usually divided into 5 groups of axioms: movement, order, continuity, combination and parallelism of Euclid.
In thirteen books of "Beginnings" the scientist presented arithmetic, solid geometry, planimetry, relations according to Eudoxus. It should be noted that the presentation in this work is strictly deductive. Definitions begin each book of Euclid, and in the first of them they are followed by axioms and postulates. Next come sentences divided into problems (where something needs to be built) and theorems (where something needs to be proven).
Flaw of Euclid's mathematics
The main drawback is that the axiomatics of this scientist is not complete. The axioms of motion, continuity and order are missing. Therefore, the scientist often had to trust the eye, resort to intuition. Books 14 and 15 are later additions to the work written by 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 are the fruit of the collective work of the school led by the scientist.
Further development of science
AppearanceEuclidean 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) - Russian mathematician who made an important discovery. He noted that there is a geometry that differs from Euclidean. This 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 Euclid's Elements 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 the 1860s. Among the letters were rave reviews of the scientist about the geometry of Lobachevsky.
Other works of Euclid
Very great 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 withstood alreadymore than five hundred publications 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, 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 "given". Another work of Euclid is a book on optics, which contains information about perspective. The scientist of interest to us wrote an essay on catoptrics (he outlined in this work the theory of distortions that occur in mirrors). There is also a book by Euclid called "Division of Figures". Unfortunately, the work on mathematics "On False Conclusions" has not been preserved.
So, you met such a great scientist as Euclid. We hope you found his short biography useful.
