(330 BC - 275 BC) Greek mathematician. Along with later, Archimedes and Apollonius of Perga, Euclid was soon included in the triad of the great mathematicians of antiquity. However, in the light of the immense influence that his work would have throughout history, should also consider it as one of the most illustrious of all time.
Even though he made contributions and corrections of relief, Euclid has been viewed sometimes as a mere compiler of Greek mathematical knowledge. In fact, the great merit of Euclid resides in its work of systematization: based on a series of definitions, postulates and axioms, established by rigorous logical deduction all harmonious building of Greek geometry. Judged not without reason as one of the highest products of why human and admired as a finished and perfect system, Euclidean geometry would remain in force for over twenty centuries, until appeared, already in the 19th century, calls noneuclidean geometries.
Little is known for certain of the biography of Euclid, despite being the most famous mathematician of antiquity. It is likely that you become educated in Athens, which would explain their good knowledge of the geometry developed in the school of Plato, although it does not seem to be familiar with the works of Aristotle.
Euclid taught in Alexandria, where she opened a school which would end up being the most important of the Hellenistic world, and reached great prestige in the exercise of their teaching during the reign of Ptolemy I Soter, founder of the Ptolemaic Dynasty who would rule Egypt from the death of Alexander the great to the Roman occupation. There the King required him to would show him a fast-track procedure to access the knowledge of mathematics, to which Euclid replied there is a via regia to geometry. This Epigram, however, is also attributed to the mathematician Menaechmus, as a reply to a similar demand by Alexander the great.
Tradition has preserved an image of Euclid as a man of remarkable kindness and modesty, and has also aired an anecdote relating to his teaching, collected by Juan Estobeo: a young novice on the study of geometry asked him what would win with their learning. Euclid explained that the acquisition of knowledge is always valuable in itself; and since the boy had the claim to get some out of his studies, he ordered a servant to give him a few coins.
The elements of Euclid
Euclid was the author of various treaties, but his name is mainly associated to one of them, elements, rivaling its broadcast with the most famous works of literature, such as the Bible or the Don Quixote. He is, in essence, a compilation of works by earlier composers (notably Hippocrates of Chios), which passed immediately by its general plan and the magnitude of its purpose.
Of the thirteen books that compose it, the first six correspond to what is understood as plane geometry or elemental. In Euclides collects the geometric techniques used by the Pythagoreans to resolve what today are considered examples of linear and quadratic equations; also includes the general theory of proportion, traditionally attributed to Eudoxus.
Books from the seventh to the tenth try numerical issues: the main properties of the theory of numbers (divisibility, primes), the concept of commensurability of segments to its squares and issues related to the transformations of the radical doubles. The remaining three are concerned with the geometry of solids, culminating in the construction of the five regular polyhedrons and its circumscribed spheres, which had already been studied by Theaetetus.
Of the remaining works of Euclid we only have references or brief summaries of subsequent commentators. Treaties and the conical surface places already contained, apparently, some of the results subsequently exposed by Apollonius of Perga. The Porismas develop the geometric theorems now called projective type; This work is only kept the summary drawn up by Alexandria Pappo. In optics and Catoptrica is studying the laws of perspective, the propagation of light, and the phenomena of reflection and refraction.
Two thousand years
The subsequent influence of the elements of Euclid was decisive; After his appearance, it was adopted immediately as exemplary textbook in the initial teaching of mathematics, whereupon the purpose which must inspire Euclid was fulfilled. After the fall of the Roman Empire, his work was preserved by the Arabs and again widely reported from the Renaissance.
Even apart from the strictly mathematical field, Euclid was taken as a model, in its method and exposure, by authors such as Galen, for medicine, or Spinoza, ethics. This is not counting the multitude of philosophers and scientists of all ages who, in their search for explanatory systems of universal validity, had in mind the admirable logical rigour of the geometry of Euclid.
In fact, Euclid established what, from his contribution, he was supposed to be the classic form of a mathematical proposition: a sentence logically deduced from previously accepted principles. In the case of elements, the principles that are taken as a starting point are 23 definitions, five postulates and five axioms or common notions.
The nature and scope of these principles have been the subject of frequent discussion throughout history, especially so it refers to the postulates and, in particular, to the fifth postulate, called the parallel. According to this assumption, by an external point to a straight only can be traced a parallel to this line. Their different status with regard to the remaining postulates was already perceived from the same seniority, and there were different attempts to prove the fifth postulate as a theorem.
The efforts to find a demonstration were unsuccessful and continued until the 19th century, when some unpublished works of Carl Friedrich Gauss (1777-1855) and the Russian mathematician Nikolai Lobachevski (1792-1856) investigations showed that it was possible to define a geometry perfectly consistent (hyperbolic geometry) in which the fifth postulate was not fulfilled. Thus began the development of noneuclidean geometries, notably the elliptical geometry of the German mathematician Bernhard Riemann (1826-1866), judged by Albert Einstein as which best represents the model of relativistic space-time.