The Euclides contributions To mathematics are of such importance that until today they remain in force, after more than 2000 years of being formulated.
Euclid of Alexandria, a name that refers to the mathematician to distinguish it from the namesake Euclides de Megara, was a Greek who laid important bases for mathematics and geometry.
Euclid, 300 a.c.
The contributions of Euclides have led to the development of a large number of works in different sciences.
That is why it is common to find disciplines that contain the adjective"Euclidian"in their names, since they base part of their studies on the geometry described by Euclid.
Main contributions of Euclides
Elements
The most recognized contribution of Euclides has been his work titled"Elements". In this work, Euclides collected an important part of the mathematical and geometric developments that had been realized in his time.
In"Elements", Euclides also develops own concepts that have been of great importance, such as the algorithm of Euclid and several issues of the theory of numbers.
The work"Elements"is considered a classic of science, compared with the works"Principia"of Newton.
Among the highlights of"Elements"are the 5 Euclidean postulates.
Euclid's algorithm
In his work"Elements", Euclid described a method for finding the most common divisor between two numbers.
This algorithm has been of great importance for mathematics and has found application in various fields of human activity, especially in economy .
Many other algorithms have been developed from Euclid's algorithm for applications in other fields or for more efficient processes.
Among them the binary Euclidean algorithm and the modified Euclidean algorithm.
Euclidian Geometry
The contributions of Euclid were mainly in the field of geometry. The concepts developed by him dominated the study of geometry for almost two millennia.
It is difficult to give an exact definition of what Euclidean geometry is. In general, this refers to the geometry that encompasses all the concepts of classical geometry, not only Euclid's developments, although he has compiled and developed several of these concepts.
Some authors assert that the aspect in which Euclides contributed more to the geometry was its ideal of founding it in an incontestable logic.
Moreover, given the limitations of the knowledge of his time, his geometrical approaches had several shortcomings that later other mathematicians reinforced.
Demonstration and mathematics
Euclid, along with Archimedes and Apolinius, are considered the perfectioners of the demonstration as a chained argument in which a conclusion is reached while each link is justified.
Demonstration is fundamental in mathematics. It is considered that Euclides developed the processes of mathematical demonstration in a way that lasts until today and that is essential in modern mathematics.
Axiomatic Methods
In the presentation of geometry made by Euclid in"Elements", Euclides is considered to formulate the first"axiomatization"in a very intuitive and informal way.
Axioms are basic definitions and propositions that do not require proof. The way in which Euclid presented the axioms in his work subsequently evolved into an axiomatic method.
In the axiomatic method, definitions and propositions are posed so that each new term can be eliminated by previously introduced terms, including axioms, to avoid infinite regression.
Euclid indirectly raised the need for a global axiomatic perspective, which propitiated the development of this fundamental part of modern mathematics.
References
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- Cornelius M. Euclid Must Go? Mathematics in School. 1973; 2 (2): 16-17.
- Fletcher W.C. Euclid. The Mathematical Gazette 1938: 22 (248): 58-65.
- Florian C. Euclid of Alexandria and the Bust of Euclid of Megara. Science, New Series . 1921; 53 (1374): 414-415.
- Hernández J. More than twenty centuries of geometry. Book Review. 1997; 10 (10): 28-29.
- Meder A. E. What is Wrong with Euclid? The Mathematics Teacher . 1958; 24 (1): 77-83.
- Theisen B. Y. Euclid, Relativity, and sailing. History Mathematica . 1984; eleven : 81-85.
- Vallee B. The complete analysis of the binary Euclidean algorithm. International Algorithmic Number Theory Symposium. 1998; 77-99.