# 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).

# Metric geometry : Investment beam circumferences

Transformation through investment in geometric shapes grouped elements can be of interest to use the investment as a tool for analysis in complex problems. In this case study transforming “beams circumferences corradicales” through various investments that transform. Later these transformations need to solve the problem “Apolonio” (circumference with three tangency constraints) o la “Generalization of the problem of Apollonius” (circumferences with three angular restrictions).

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

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.

# Metric geometry : Investment in the plane

The investment is a homographic transformation that preserves the angular relationships (is in accordance). Its main application is the determination of geometry problems with angular conditions including solving are tangents exercises.