Las técnicas de solución de problemas basadas en la intersección de lugares geométricas se suelen asociar a problemas sencillos de la geometría clásica.
En estos casos es el planteamiento de la solución lo que entraña la mayor complejidad, ya que los lugares geométricos derivados suelen ser elementos geométricos sencillos.
Determinar un punto P desde el que se observe bajo el mismo ángulo a los tres lados de un triángulo ABC.
Vamos a resolver el problema de determinar un cuadrado, cuyos vértices se encuentran sobre elementos geométricos dados.
En particular fijaremos los correspondientes a una de sus diagonales sobre una recta, otro de los vértices en una recta diferente y el cuarto vértice sobre una circunferencia.
Los problemas básicos de geometría métrica tienen una especial belleza. Son adecuados para introducir a los alumnos en el arte del análisis en esta disciplina.
Uno de los problemas propuestos en el examen de Selectividad de Septiembre de 2014 plantea la obtención de una figura geométrica simple, un cuadrado, cuyos vértices se encuentran sobre elementos geométricos dados.
By raising the issue of the pool table, that is to hit one of the two balls that are on the table (A for example) , so that it impacts the other (la B) previously given in one of the bands (edges) Table, flipping the closed problem to a simple bounce case.
We can generalize the problem considering that you can give, before impact with the second ball, a given number of impacts with the bands (lateral edges) Table.
Geometric figures can be compared with each other by reference for this comparison both its shape and its size.
Based on the different combinations that can be found in these comparisons will classify in:
Similar forms: Have the same shape but different size
Equivalent forms: They have different but equal size (Volume of the area)
Congruent shapes: Have the same shape and size (equal)
Overall, to obtain a form equivalent to another given, use an equivalent square as intermediate between two equivalent figures. Thus, first discuss how to obtain a square equivalent to a geometric figure.
Gervalengar YouTube user has an educational channel dedicated to the display of descriptive geometry. In his instructional videos presents descriptive geometry constructions (Representation systems) animated form, showing the spatial patterns and its projection on the planes dihedral classical discipline to address this from a purely visual level.
The surfaces used in the engineering are different natures. Su classification based on different criteria serves to facilitate understanding and su deduce common groups ellas.
One aspect which differentiates these surfaces is the possibility of generating by straight movement along a curve, or subject to a law of generation. These include the so-called “Hyperbolic paraboloid”
The concept of power is fundamental to solving problems in a structured way and generalization of tangency where angularity.
This concept, initially apply the fundamental problem of tangents, allow us to use a systematic analysis of different cases, because we can reduce the remaining exercises tangent circles to three given to a single basic problem.
In this presentation, made with Prezi, the basic ideas associated with this important concept is.
One of the first problems we must learn to work in projective geometry is the determination of homologous elements, both in series and in bundles and in any provision of bases, or separate superimposed.
To continue the study of the methodology to be used will use the dual model the elements based on “points”, ie with straight, further assuming that the bases of the respective beams are separated relate.
Projective definition of the conical allowed to start solve classical problems of identification of new elements of the conical (new points and tangents in them), and find the intersection with a line or a tangent from an external point. These problems can be solved by various more or less complex methods and conceptually more or less laborious paths.
We will now see how to determine the two possible intersection points of a line with a taper defined by five points.
When the base of a series is a conical series is second order.
As in the case of series of the first order when the overlapping series were defining, we can establish proyectividades between two sets of second order with the same base (in this case a conical).
