Graphic PIZiadas

Graphic PIZiadas

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Categories Tangencies

Problem of Apollonius : ccc

Any of the problems of tangents that are included under the name "Apolonio problems" can be reduced to one of the variants studied the most basic of them all: the fundamental problem of tangents (PFT).

In this case we will study what we call "Apolonio Case ccc", namely, If the problem of tangents in which the data are given by conditions tangents three circumferences (ccc).

Conic as Locus Centers Circumferences Tangents

We have seen that the study of conic can be made from different geometric approaches. En particular, to start analyzing conic we have defined as the ellipse locus, we said that:

Ellipse is the locus of points in a plane whose sum of distances from two fixed points, called Spotlights, It has a constant value.

This metric definition of this curve allows us to address important study relating to the tangents circumferences, known as “Problem of Apollonius” in any of its versions. When we approach the study of the parabola or hyperbola return to reframe the problem to generalize these concepts and reduce problems “fundamental problem of tangents in the case straight”, or “fundamental problem of tangents in the case circumference”, namely, determining a circumference of a “Make corradical” a tangency condition.

Apollonius and his ten problems

One of the most comprehensive articles they have written my students in geometry classes is describing how to solve the so-called “Apollonius problems”.

Determining come straight circumferences or geometric constraints defined by the tangents are based on a family of geometric problems of great interest.

Metric geometry : Generalization of the fundamental problem of tangents :

We have solved the fundamental problem we have called for tangents when presented with tangency conditions on a circle or a straight. Conceptually we can assume that both problems are the same, if we consider the straight as a circle of infinite radius. The statement therefore posed circumferences obtaining through two points were tangent to a straight or tangent to a circle.

Metric geometry: Circunferencias con condiciones angulares. Solución al Problema I

From the different solutions to the problem are proposed to obtain circumferences with angular conditions ( passing through a point, are tangent to a circle, forming an angle with a straight), we will analyze this solution using the application of the concepts of power used in the “Fundamental Problem Tangencies” ( PFT ).

The general model search can be the first step of a surveyor training. Later we discuss specific ways this particular problem that could simplify the tracking.

Metric geometry : Investment : Application to the resolution of problems and angular tangents

Application inversion

Investment is a transformation that can solve problems with angular conditions. It can be applied directly or used to reduce other problems addressed simplest known nature.

The different approaches with which we can deal with a problem will be studied by developing a simple classic problem of tangents.