Geometría

Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes. Geometry began to see elements of formal mathematical science emerging in Greek mathematics as early as the 6th century BC. By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment, The Elements, set a standard for many centuries to follow. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC. Islamic scientists preserved Greek ideas and expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid analytic footing by mathematicians such as René Descartes and Pierre de Fermat. Since then, and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, describing spaces that lie beyond the normal range of human experience. While geometry has evolved significantly throughout the years, there are some general concepts that are fundamental to geometry. These include the concepts of point, line, plane, distance, angle, surface, and curve, as well as the more advanced notions of topology and manifold. Geometry has applications to many fields, including art, architecture, physics, as well as to other branches of mathematics.

La geometría es una rama de las matemáticas que se ocupa del estudio de las propiedades de las figuras en el plano o el espacio, incluyendo: puntos, rectas, planos, politopos (que incluyen paralelas, perpendiculares, curvas, superficies, polígonos, poliedros, etc.). Es la base teórica de la geometría descriptiva o del dibujo técnico. También da fundamento a instrumentos como el compás, el teodolito, el pantógrafo o el sistema de posicionamiento global (en especial cuando se la considera en combinación con el análisis matemático y sobre todo con las ecuaciones diferenciales). Sus orígenes se remontan a la solución de problemas concretos relativos a medidas. Tiene su aplicación práctica en física aplicada, mecánica, arquitectura, geografía, cartografía, astronomía, náutica, topografía, balística etc., y es útil en la preparación de diseños e incluso en la fabricación de artesanía.