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April Archive 2018

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.

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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.

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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).

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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.

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