First traces of geometry
If Greek the can be regarded as the founders of the Géométrie as a science and mathematical discipline, of many knowledge in geometry, necessary to the Topographie, the Architecture, the Astronomie and the Agriculture, however preceded Greek civilization. The first recognized concepts of geometry go back to 3000 AJC, under the old Egypt, old Hindu civilization and the babyloniens.
Egyptian and Babylonian geometries
The Egyptian pyramids and the plans of irrigation testify to a knowledge at least empirical to the plane figures and solids. The first results were a whole of empirical principles concerning the lengths, the angles, the surfaces and volumes; they were developed for the needs for the Architecture, the Agriculture and the Astronomie. Among these results, one can quote versions of the Théorème of Pythagore, developed by the Egyptians and the Babylonians 1500 years before Pythagoriciens, a table of trigonometry at the Babylonians, or the exact formula of the volume of a truncated square pyramid.The pre-Babylonian Tablette YBC 7289 going back to -1700 ± 100 testifies to the first questionings on calculation the lengths and gives a good approximation length of the diagonal of a square.
Geometry sumérienne
The discovery of the Tablette of Plimpton 322 tends to show that the theorem of Pythagore was probably known civilization sumérienne 1000 years before Pythagore.
Indian geometry (3000-500 AJC)
The Civilization of the valley of Indus developed results of geometry as developed as their contemporaries in Mésopotamie and Egypt. This development was partly developed by town planning: the streets draw in the cities of the squarings, with the image of the current American cities.
Chinese geometry
the Last nine Chapters on mathematical art , text fundamental of knowledge of Chinese civilization, offer calculations of surfaces and volumes, and a formulation of the theorem of Pythagore.
The Greek heritage
Greek geometry (600-300 AJC)
See also: Greek Geometry--> For the mathematicians of ancient Greece, the geometry was the heart of sciences, reaching a richness of unequalled methodology in the other fields of knowledge. They studied new figures, of which curves, surfaces and solids. They recognized that the physical objects are only approximations of the forms studied in geometry.
Thalès de Milet and Pythagore is known to be among the first to develop a hypothético-deductive reasoning and to wonder about the value of the reasoning. One generally allots at Thalès the equality opposed angles, the equality of the angles at the base of an isosceles triangle, the study of the inscribed angles and the theorem of Thalès. One allots to the pythagoricians the proof of the theorem known as of Pythagore, and the figuration of the integers.
Plato introduces the five solids known as Platonic: the tetrahedron, the cube, the octahedral one, the Isocaèdre and the dodecahedron. The proportions and incommensurability are introduced by Euxode. Euclide summarizes in its Elements in a precise and rigorous way the principal work known at its time in geometry. But this treaty does not include/understand the calculation of the surfaces and volumes.
In addition, Plato, although not mathematician, introduced the idea that all the geometrical figures can be built using a not graduated rule and of a perfect compass. Then posed problems such as the Trisection of the angle, the Quadrature of the circle, and the Duplication of the cube. This last problem, encouraged Ménechme to introduce the Conique S.
Probable origin
The origin of the geometry, like the origin of the Science, is prone to discussion according to its meaning. Traditionally, the first work of geometry goes up with the ancient Greece. Indeed, the Éléments of Euclide are incontestably the axiomatic first formulation of the geometry.
Hellenistic geometry (300 before our era - 500 of our era)
The geometry hellenist starts with the writing of the elements of Euclide. A system of axioms for the Euclidean geometry is presented. The elements do not summarize knowledge in geometry of the time.
Contribution of Arabic
In addition to the translation of the Greek texts through which Europe rebuilds the Greek heritage, the mathematicians of Arab language strongly developed the Trigonométrie. One allots the goniometrical functions introduced by Nasir Al-Din Al-Tusi, the formula to them of Al Kashi, the thorough approximations of pi, etc
The mathematicians of Arab language were the first to apply an algebraic approach to parameterize the curves, and to solve problems of geometry by calling upon the polynomial algebra. Sometimes they are thus regarded as the precursors of the algebraic Géométrie.
Birth of the analytical geometry
See also: analytical Geometry
August 1st
Geometry at the 19th century
NonEuclidean geometry
See also: nonEuclidean Geometry
Until the 19th century only one geometry, based on the axioms of Euclide was studied, and which was regarded as the true geometry of physical space. The discovery of nonEuclidean geometries by Gauss, Lobatchevsky, Bolyai modified this apprehension of absolute space completely.
Various types of geometries took their autonomy then: hyperbolic Geometry, elliptic Geometry, each one being based on a model different of space. More important still than the models allowing the concrete realization of a geometry, is the set of axioms to which one can bring back it.
August 1st
The program of Erlangen
The Program of Erlangen, published in 1872 comparative pennies the title “Consideration on modern geometrical research”, is the work of Felix Klein. It is an important work of synthesis which validates the not-Euclidean geometries and gives to the projective geometry a central role. This work constitutes a third approach of the geometry by the Théorie of the groups. According to the design of Klein, the geometry is the study of spaces of points on which operate Groupe S of transformations (also called symmetries) and quantities and properties which are invariant for these groups.See also: Program of Erlangen
Geometry at the 20th century
August 1st
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