The origin of the term geometry is an accurate description of the work of early surveyors who were interested in issues such as the size of the fields or the drawing of angles straight to the corners of buildings. This type of empirical geometry that flourished in ancient Egypt, Sumeria and Babylon, was refined and systematized by the Greeks.
geometric knowledge of the Babylonians: By 2200 BC the rules applied to calculate areas of rectangles, isosceles triangles, trapezoids and circles. In the measurement of solids, gave solutions related to parallelepipeds, cylinders and prisms, which applied to excavation of canals for irrigation. They knew also that the angle inscribed in a semicircle is right, the homologous sides of similar triangles are proportional, the relationship between the sides of a triangle and the relationship between the circumference of a circle to its diameter, taking value of 3 for p.
In the sixth century BC mathematician Pythagoras laid the cornerstone of cinetífica geometry to show that the various arbitrary and disparate laws of empirical geometry can be deduced as logical onclusions a limited number of axioms or postulates. These principles were regarded by Pythagoras and his disciples as self-evident truths, but in modern mathematical thinking are considered as a set of useful but arbitrary assumptions.
Although there are previous attempts, the first systematic body of knowledge that crystallized the elements of Euclid (300 BC), but did not understand all the mathematical knowledge of the time, its structure is so strong that even today, organic is the base of elementary geometry texts. Apollonius of Perga
studied the family of curves known as conic and discovered many of their fundamental properties. Conics are important in many fields of physical sciences, for example, the orbits of the planets around the sun are essentially conical.
Archimedes, one of the great Greek scientists made a considerable number of contributions to geometry. He invented ways to measure the area of \u200b\u200bshapes and curves the surface and volume of solids bounded by curved surfaces such as paraboloids and cylinders. It also developed a method to calculate an approximation of the value pi, the ratio between the diameter and circumference of a circle and established that this number was between 3 10/70 and 3 10/71.
Thus, Euclid, Archimedes and Apollonius, Greek geometry reached its culmination. The geometry advanced little since the end of the Greek era to the Middle Ages.
The next important step in this science was given by the philosopher and mathematician Rene Descartes, whose treatise Discourse on Method, published in 1637, he made time. This work forged a connection between geometry and algebra by showing how to apply the methods of a discipline on the other. This is a foundation of analytic geometry, in which the figures are represented by algebraic expressions, subject underlying most of modern geometry. Another important development
seventeenth century was the investigation of the properties of geometric figures that remain unchanged when the figures are projected from one plane to another. The geometry underwent a radical change of direction in the nineteenth century.
mathematicians Carl Friedrich Gauss, Nikolai Lobachevsky and János Bolyai, working separately, coherent systems developed non-Euclidean geometry. These systems came from work on the so-called "parallel postulate" of Euclid, to propose alternatives that generate foreign models and non-intuitive space, although consistent.
geometric knowledge of the Babylonians: By 2200 BC the rules applied to calculate areas of rectangles, isosceles triangles, trapezoids and circles. In the measurement of solids, gave solutions related to parallelepipeds, cylinders and prisms, which applied to excavation of canals for irrigation. They knew also that the angle inscribed in a semicircle is right, the homologous sides of similar triangles are proportional, the relationship between the sides of a triangle and the relationship between the circumference of a circle to its diameter, taking value of 3 for p.
In the sixth century BC mathematician Pythagoras laid the cornerstone of cinetífica geometry to show that the various arbitrary and disparate laws of empirical geometry can be deduced as logical onclusions a limited number of axioms or postulates. These principles were regarded by Pythagoras and his disciples as self-evident truths, but in modern mathematical thinking are considered as a set of useful but arbitrary assumptions.
Although there are previous attempts, the first systematic body of knowledge that crystallized the elements of Euclid (300 BC), but did not understand all the mathematical knowledge of the time, its structure is so strong that even today, organic is the base of elementary geometry texts. Apollonius of Perga
studied the family of curves known as conic and discovered many of their fundamental properties. Conics are important in many fields of physical sciences, for example, the orbits of the planets around the sun are essentially conical.
Archimedes, one of the great Greek scientists made a considerable number of contributions to geometry. He invented ways to measure the area of \u200b\u200bshapes and curves the surface and volume of solids bounded by curved surfaces such as paraboloids and cylinders. It also developed a method to calculate an approximation of the value pi, the ratio between the diameter and circumference of a circle and established that this number was between 3 10/70 and 3 10/71.
Thus, Euclid, Archimedes and Apollonius, Greek geometry reached its culmination. The geometry advanced little since the end of the Greek era to the Middle Ages.
The next important step in this science was given by the philosopher and mathematician Rene Descartes, whose treatise Discourse on Method, published in 1637, he made time. This work forged a connection between geometry and algebra by showing how to apply the methods of a discipline on the other. This is a foundation of analytic geometry, in which the figures are represented by algebraic expressions, subject underlying most of modern geometry. Another important development
seventeenth century was the investigation of the properties of geometric figures that remain unchanged when the figures are projected from one plane to another. The geometry underwent a radical change of direction in the nineteenth century.
mathematicians Carl Friedrich Gauss, Nikolai Lobachevsky and János Bolyai, working separately, coherent systems developed non-Euclidean geometry. These systems came from work on the so-called "parallel postulate" of Euclid, to propose alternatives that generate foreign models and non-intuitive space, although consistent.
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