Graphic PIZiadas

Graphic PIZiadas

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The problem of the CAP with three forms

One of the first problems posed in my classes is that call “The CAP with three forms”.

It serves as introduction to the descriptive geometry and forces to make a spatial analysis of great interest for the training of students.

The problem is to determine a plug used to fill three holes that we have made in a wooden box.

Canal de YouTube : Descriptive geometry

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.

Metric geometry : Problem of Apollonius : rcc

Any of the problems of tangents that are included under the denomination of “Apollonius problems” can be reduced to one of the studied variants of the most basic of all: the fundamental problem of tangents (PFT).
In all these problems we will consider fundamental objective to reduce the problem to propose to one of these critical cases, by changing the constraints that define other concepts based on the orthogonality.

In this case we will study what we call “Case Apollonius RCC”, namely, For the problem of tangency at which the data are given by condition of tangency to a line (r) and two circles (cc).

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).

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.

Representation systems : Projections [ Descriptive geometry ]


The so-called representation systems encompasses a set of techniques and projection models for viewing items in a three dimensional space on a two dimensional plane.

Each of the systems provides a number of advantages that make it particularly useful in certain applications. So, systems that are included in the set of perspectives, are especially useful to give a simple three-dimensional view of the object. Cylindrical nature systems facilitate operations orthogonal measure to reduce them to obtain Pythagorean triangles (rectangles), models while central conical or approximate how the human eye works.