Biography of Euclid
Euclid was a famous mathematician, who is usually called the “father of geometry.”
Childhood and early years
Euclid was born about 330 BC. e., presumably, in the city of Alexandria. Some Arab authors believe that he came from a wealthy family from Nokrat. There is a version that Euclid could have been born in Tire, and spend his entire future life in Damascus. According to some documents, Euclid studied at the ancient school of Plato in Athens, which was only possible for wealthy people. Already after that, he will move to Alexandria in Egypt, where he will begin the division of mathematics, now known as “geometry.”
The life of Euclid of Alexandria is often confused with the life of Euclid from Meguro, which makes it difficult to find any reliable sources for the life of a mathematician. It is known only that he attracted the attention of the public to mathematics and brought this science to an entirely new level, having made revolutionary
Scientific activity
Euclid reasonably considered “the father of geometry.” It was he who laid the foundations of this field of knowledge and raised it to the proper level, having discovered to the society the laws of one of the most difficult sections of mathematics at that time. After moving to Alexandria, Euclid, like many scholars of the time, prudently spends most of the time at the Alexandria Library. This museum, dedicated to literature, art and science, was founded by Ptolemy. Here, Euclid begins to integrate geometric principles, arithmetic theories and irrational numbers into a unified science of geometry. He continues to prove his theorems and reduces them to the colossal work of the “Beginning.” For all the time of his little researched
His work contains more than 467 statements regarding planimetry and stereometry, as well as hypotheses and theses that advance and prove his theories with respect to geometric representations. It is for certain known that as one of the examples in his “Elements” Euclid used the Pythagorean theorem, which establishes the relationship between the sides of a right triangle. Euclid argued that “the theorem is true for all cases of right-angled triangles”. It is known that during the existence of “Elements”, until the XX century, more copies of this book were sold than the Bible. “Beginning”, published and republished countless times, different mathematicians and authors of scientific works used in their work. Euclidean geometry knew no boundaries, and the scientist continued to prove all the new theorems in completely different areas, as, for example, in the field of “prime numbers”, and also in the arithmetic knowledge base. A chain of logical reasoning Euclid sought to open secret knowledge to mankind. The system, which the scientist continued to develop in his “Elements”, will become the only geometry that the world will know until the 19th century. However, modern mathematicians have discovered new theorems and hypotheses of geometry, and divided the subject into “Euclidean geometry” and “non-Euclidean geometry.” becomes the only geometry that the world will know until the 19th century. However, modern mathematicians have discovered new theorems and hypotheses of geometry, and divided the subject into “Euclidean geometry” and “non-Euclidean geometry.” becomes the only geometry that the world will know until the 19th century. However, modern mathematicians have discovered new theorems and hypotheses of geometry, and divided the subject into “Euclidean geometry” and “non-Euclidean geometry.”
The scientist himself called this the “generalized approach”, based not on the method of trial and error, but on the presentation of undeniable facts of theories. At a time when access to knowledge was limited, Euclid was committed to studying issues of completely different areas, including “arithmetic and numbers.” He concluded that the discovery of “the largest prime number” is physically impossible. This statement he justified by the fact that if one is added to the largest known prime number, this inevitably leads to the formation of a new prime number. This classic example is proof of the clarity and accuracy of the scientist’s thought, despite his venerable age and the times in which he lived.
Axioms
Euclid said that the axioms are statements that do not require proof, but at the same time he understood that blind acceptance of these statements on faith can not be used in constructing mathematical theories and formulas. He realized that even axioms should be backed up by undeniable evidence. So the scientist began to give logical conclusions that confirmed his geometric axioms and theorems. For a better understanding of these axioms, he divided them into two groups, which he called “postulates.” The first group is known as “general concepts”, consisting of recognized scientific statements. The second group of postulates is synonymous with the geometry itself. The first group includes such concepts as “the whole is greater than the sum of parts” and “if two values are separately equal to the same third, then they are equal to each other”. Here are just two of the five postulates written by Euclid. The five postulates of the second group refer directly to geometry, arguing that “all right angles are equal to each other,” and that “from every point to every point one can draw a straight line.”
Scientific activity mathematics Euclid flourished, and in the early 1570’s, his “Principles” were translated from Greek into Arabic, and then into English by John Dee. Since its writing, “Nachala” has been reprinted 1,000 times and, in the end, took a place of honor in the classrooms of the 20th century. There are many cases when mathematicians tried to challenge and refute Euclid’s geometric and mathematical theories, but all attempts invariably ended in failure. The Italian mathematician Girolamo Saccheri sought to improve the works of Euclid, but abandoned his attempts, unable to find in them the slightest flaw. And only after a century a new group of mathematicians can present innovative theories in the field of geometry.
Other jobs
Without ceasing to work on changing the theory of mathematics, Euclid managed to write a number of works on a different subject, which are used and referenced to this day. These works were pure assumptions based on irrefutable evidence, a red thread passing through all the “Beginnings”. The scientist continued his study and opened a new field of optics – a catoptric, which to a large extent asserted the mathematical function of mirrors. His work in the field of optics, mathematical relationships, systematization of data and the study of conic sections have been lost in the depths of centuries. It is known that Euclid successfully graduated eight editions or books, according to theorems concerning conic sections, but none of them has reached our days. He also formulated hypotheses and assumptions based on the laws of mechanics and the trajectory of motion of bodies. Apparently, all these works were interrelated, and the theories expressed in them grew out of a single root – his famous “Beginnings.” He also developed a series of Euclidean “constructions” – the basic tools needed to perform geometric constructions.
Personal life
There is evidence that Euclid opened a private school at the Alexandria Library in order to be able to teach mathematicians the same enthusiasm as himself. There is also an opinion that in the later period of his life he continued to help his students in developing their own theories and writing works. We do not even have a clear idea of the appearance of the scientist, and all the sculptures and portraits of Euclid, which we see today, are only a figment of the imagination of their creators.
Death and heritage
The year and causes of Euclid’s death remain a mystery to humanity. In the literature there are vague hints that he could die around 260 BC. e. The legacy left to the scientist after himself is far more significant than the impression he made during his lifetime. His books and works were sold all over the world until the XIX century. The legacy of Euclid experienced the scientist for as many as 200 centuries, and served as a source of inspiration for such personalities as, for example, Abraham Lincoln. According to rumors, Lincoln always superstitiously carried the “Beginning”, and in all his speeches he cited the works of Euclid. Even after the death of the scientist, mathematicians from different countries continued to prove the theorems and publish works under his name. In general, in those times when knowledge was closed to the masses, Euclid, by logical and scientific way, created the format of mathematics of antiquity,
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