# 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.

# The false position method. Application of overlapping series of second order.

The theoretical models of projective geometry can be proposing problems that are not of direct application. We will have that “dress up” therefore exercises to infer in the student further analysis and a transverse treatment of knowledge: Can I apply what they learn to solve this problem?.
After analyzing in detail the operations with overlapping series of second order, Let's see an example of application which does not consist in obtaining new tangents or points of contact of a conical.

# Determinación de un segmento conocido su punto medio [Solución]

Al plantear un problema de geometría métrica podemos abordar su resolución con diferentes estrategias. para ilustrar uno de estos métodos vamos a resolver el de determinar un segmento del que se conoce su punto medio junto con otras restricciones adicionales.

En particular analizaremos el caso en el que los extremos del segmento se encuentran situados sobre dos circunferencias coplanarias de radio arbitrario.

# The problem of the two peoples and the bridge

One of the first problems of geometry metric I propose to my students is to start the geometric model analysis while we review the basic transformations studied in earlier.

The problem is posed as a real case study, spiced up with a story that varies as a deeper analysis, and I jokingly call “The Cool River Bridge”, or “problem of the two peoples and the bridge”.