GEOMETRÍA ELEMENTAL EUCLIDIANA. Geometría Elemental Básica. Rectas y planos. Axiomas y relaciones de incidencia. Segmentos, rayos y ángulos; triángulos y polígonos. Congruencias y semejanzas Convexidad. y separación. Principales teoremas de la geometría elemental. Introducción a la teoría de la medida para áreas y volúmenes. Didáctica de la Geometría Elemental. Resuelve problemas de forma, movimiento y localización.
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2019-08-13
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Universidad Nacional de Educación Enrique Guzmán y Valle
Abstract
El objetivo fundamental de este trabajo de investigación es dar a conocer que en las diferentes antiguas civilizaciones de la humanidad, el afán por medir la
tierra, el interés por las grandes construcciones, saber cuándo sembrar, cuando cosechar y
el tratar de predecir acontecimientos futuros a través de los astros llevó al desarrollo de la
Astronomía y, previamente, al desarrollo de la Geometría.
Con Euclides se pasó de la exploración y de la experiencia a las deducciones
racionales, la Geometría pasó a ser una ciencia deductiva, partiendo de definiciones,
axiomas y postulados.
En su obra monumental Los Elementos, Euclides muestra su creatividad, lógica,
rigurosidad, didáctica, exactitud, y coherencia. Por primera vez en las matemáticas se da
la axiomatización de la Geometría: se inicia dando los conceptos de los elementos básicos:
el punto, la recta, el plano y la circunferencia; seguidamente, se enuncian una serie de
axiomas: propiedades de los objetos señalados anteriormente. Los axiomas no se pueden
demostrar, pero se aceptan como verdaderos. Estos axiomas constituyen la base de toda la
teoría, y a partir de ellos se levantan afirmaciones que se deben y pueden demostrar. En
Los Elementos, Euclides propone 5 axiomas, de los cuales el V axioma: Por un punto
exterior a una recta existe una sola paralela a la recta dad, es el que fue considerado por
muchos matemáticos por un espacio de 23 siglos que podía demostrarse a partir de los 4
anteriores axiomas, esfuerzo que resultó infructuoso. En 1899, Hilbert, en su obra
Fundamentos de la Geometría, propone 20 axiomas: siete de pertenencia, cinco de orden,
uno de paralelismo (Axioma V), seis de congruencia y uno de continuidad.
The fundamental objective of this research work is to make known that in the different ancient civilizations of humanity, the desire to measure the land, the interest in large constructions, knowing when to sow, when to harvest and trying to predict future events through through the stars led to the development of Astronomy and, previously, to the development of Geometry. With Euclid, exploration and experience went to rational deductions, Geometry became a deductive science, starting from definitions, axioms and postulates. In his monumental work The Elements of him, Euclides shows his creativity, logic, rigor, didactics, accuracy, and coherence. For the first time in mathematics, the axiomatization of Geometry is given: it begins by giving the concepts of the basic elements: the point, the line, the plane and the circumference; Next, a series of axioms are enunciated: properties of the objects indicated above. The axioms cannot be proved, but are accepted as true. These axioms constitute the basis of the entire theory, and from them affirmations are raised that must and can be demonstrated. In The Elements, Euclid proposes 5 axioms, of which the V axiom: For a point outside a line there is only one parallel to the line, is the one that was considered by many mathematicians for a space of 23 centuries that could be demonstrated to from the 4 previous axioms, an effort that was unsuccessful. In 1899, Hilbert, in his Foundations of Geometry, proposed 20 axioms: seven belonging, five order, one parallelism (Axiom V), six congruence and one continuity.
The fundamental objective of this research work is to make known that in the different ancient civilizations of humanity, the desire to measure the land, the interest in large constructions, knowing when to sow, when to harvest and trying to predict future events through through the stars led to the development of Astronomy and, previously, to the development of Geometry. With Euclid, exploration and experience went to rational deductions, Geometry became a deductive science, starting from definitions, axioms and postulates. In his monumental work The Elements of him, Euclides shows his creativity, logic, rigor, didactics, accuracy, and coherence. For the first time in mathematics, the axiomatization of Geometry is given: it begins by giving the concepts of the basic elements: the point, the line, the plane and the circumference; Next, a series of axioms are enunciated: properties of the objects indicated above. The axioms cannot be proved, but are accepted as true. These axioms constitute the basis of the entire theory, and from them affirmations are raised that must and can be demonstrated. In The Elements, Euclid proposes 5 axioms, of which the V axiom: For a point outside a line there is only one parallel to the line, is the one that was considered by many mathematicians for a space of 23 centuries that could be demonstrated to from the 4 previous axioms, an effort that was unsuccessful. In 1899, Hilbert, in his Foundations of Geometry, proposed 20 axioms: seven belonging, five order, one parallelism (Axiom V), six congruence and one continuity.
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Almanza Chavez, M. (2019). GEOMETRÍA ELEMENTAL EUCLIDIANA. Geometría Elemental Básica. Rectas y planos. Axiomas y relaciones de incidencia. Segmentos, rayos y ángulos; triángulos y polígonos. Congruencias y semejanzas Convexidad. y separación. Principales teoremas de la geometría elemental. Introducción a la teoría de la medida para áreas y volúmenes. Didáctica de la Geometría Elemental. Resuelve problemas de forma, movimiento y localización (Monografía de pregrado). Universidad Nacional de Educación Enrique Guzmán y Valle, Lima, Perú.