Graphic PIZiadas

Graphic PIZiadas

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Investment: Table mental gymnastics for determination of elements with angular conditions

We have already used one “Table Mental Gymnastics” to study investment: a set of exercises that serve to stimulate thinking, develop and maintain an agile mind, automate processes calculation and analysis etc..

We now propose to raise a similar set of problems but aimed at obtaining solutions to basic problems of geometry. In this case we will raise finding circumferences passing through a given point and angular meet conditions on two circumferences.

Learning Path Metric Geometry

In addressing the study of a science we can follow different paths that lead to learning. Chaining concepts linked to each other allow us to generate a mental representation of abstract patterns, facilitating their assimilation and subsequent application in problem solving.
In these pages two images that summarize a possible strategy or sequence of progressive incorporation of the basics of this branch of science in the education of our students are proposed.

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).

Geometría proyectiva: Obtaining the conical center

For the conical center will need to have poles and polar respect thereof. In particular constructions are simplified if we know tangents and contact points. We will see that is especially immediately if three tangents and their respective contact points are known, obtained from the definition of the conic by 5 data and application of the techniques disclosed to determine tangents and points of tangency.

Investment: Table mental gymnastics processing elements

What is a table of mental gymnastics? We can say that is a set of exercises that serve to stimulate reasoning, develop and maintain an agile mind, automate processes calculation and analysis etc..
In the subjects of geometry we can propose a problem and make slight variations to any of the data. Variability problem will create families of exercises that emphasize one or more concepts of interest.

Reversing a point. 10 constructions for obtaining [I- Metrics]

One recommendation I always do my students is to try to solve the same problem in different ways, instead of many times the same problems with almost similar statements.

We see a problem with metric or projective approaches in each case.

In one of my last classes we propose are obtaining the inverse of a point, an investment in the center and power is known. The proposed statement was as follows:

Since the square in Figure, in which one vertex is the center of inversion and the opposite vertex is a double point, determining the inverse of the point A (adjacent vertex).

Geometría proyectiva: Obtaining conical shafts from two pairs Diameters Polar Conjugates

A conical axes are those conjugates polar diameters are orthogonal to each.

We recall that two polar conjugate diameters, necessarily pass through the center O of the conical, are the polar two points unfit (located at infinity) that they are conjugated, namely, the polar of each of these points contains the other.

These pairs of elements determine an involution of diameters (polar) Conjugates will be defined when two pairs of beams know and their homologues.

Diédrico System: Distance from a point to a line

We can define the distance from a point P to a line r as the smallest of the distances from the point P to the infinite points on the line r. To determine this distance must obtain the line perpendicular to the line r from the point P and get their point of intersection I. The distance d from P to R is the minimum distance from this point to the line r.

This problem can have two different approaches to determining the solution sought.

Tetrahedrons in Blender

The solid modeling programs have basic objects called “primitive” from which can be generated by objects more complex geometric transformations, Boolean operations and editing vertices.
Knowledge of the properties of geometric figures allow us to generate other basic bodies that do not have the application, from the elements described above.

System dihedral: Fundamentals of auxiliary projections, changes in plane

To represent an object in the dihedral system usually use the projections on the three planes of the reference trihedron, as we have seen when studying the fundamentals of dihedral system.

In general it is sufficient to use only two of the three possible planes, It is represented for example by a straight projections on the horizontal plane and the vertical. Sometimes it may be desirable, or even necessary, obtain new projections in different directions projection, in which case the call her “auxiliary projections” .