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Graphic PIZiadas

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Categorías Geometría

Metric geometry : Problema fundamental de tangencias : PPc [II]

problema fundamental de tangencias PPc

The so-called fundamental problem of tangents may occur with respect tangency conditions of a circle, instead of a straight.

Conceptually we can assume that the above is a particular case of this, if we consider the straight as a circle of infinite radius.

In both cases therefore apply similar reasoning for resolution, based on the concepts learned power.

Metric geometry : Problema fundamental de tangencias : PPr

Problema fundamental de tangencias. Tangent to circle line through two points

Classically tangencies problems have been studied looking geometric constructions of each case study.

The concepts of power of a point on a circle can address the problems with a unifying approach, so that any tangency or incidences statement generally be reduced to a more generic fundamental problem tangents denominate (PFT).

Metric geometry : Theorems height and leg

Theorems cathetus Height 150

Along with the concepts of power, Geometry triangle solves proportional means obtaining by known theorems height and Hick.

Before stating these theorems and deduce, recall some basic concepts of proportionality to understand what it is that we can solve with constructs derived from these geometric models.

Metric geometry : Generalization of the concept of “Power”

generalization power concept

El concepto de potencia de un punto respecto de una circunferencia se basa en el producto de la mayor por la menor de las distancias de un punto a una circunferencia.
These distance values ​​are given in the string that contains the center of the circle and the point, namely, in diameter containing said point.
Is it possible to generalize this concept to consider other strings passing through the point P?

Metric geometry : Radical axis of two circles

The loci used to determine the solution of problems with geometric constraints. Among the conditions used are the angular nature and among them the orthogonality.
Given two circles, simply infinite set of circles that intersect orthogonally are grouped in a set called beam circumferences corradicales; These circles are centered on a line called the radical axis.

Locus of the Sum / Difference of squares of distances from two fixed points

pi

Los lugares geométricos permiten determinar puntos que satisfacen una determinada condición geométrica. Of interest in the resolution of problems in which metric or geometric restrictions.
Algunos lugares geométricos son elementales y sirven para definir figuras

SmartInversion : Kaleidocycle flying robot

smartinversion

SmartInversion es un ingenio, Festo company, able to pull in the air due to a movement called inversion in which a band formed by articulated light polyhedra, helium-filled, rotate about themselves. This constant movement, rhythmical button, is the one that gives the drive in the middle.

Geometric transformations : Correlations Vs homographies

transformations

Geometric transformations can be understood as a set of geometric operations that create a new figure from a previously given, invariants and properties obtained in these. The new figure is called “homologous” or correlative of the original depending on the nature of the transformation of its basic elements.

Metric geometry : Concepto de “Potencia de un punto respecto de una circunferencia”

Potencia de un punto respecto de una circunferencia

El concepto de potencia de un punto respecto de una circunferencia permite relacionar las nociones estudiadas en los teorema de Thales y Pitágoras y es la puerta para el estudio de los problemas de tangencias y transformaciones como la inversión.
We will use the concepts of able to arch over a segment on our shows, what is suggested by his review.
This concept is based on the product of two segment and, as discussed, It allows to determine geometrical places of great importance as for example the radical axis of two circles.

Representation systems : Incidence (Intersections) [ Descriptive geometry ]

line and plane intersection

Incidence problems trying to identify common elements of two geometric figures; can be defined as special cases of belonging.

Starting from the line and plane elements, We can apply the concepts of duality to analyze the possible problems that may occur.