Graphic PIZiadas

Graphic PIZiadas

My world is in..

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.

The geometry is not much different in this respect to other disciplines yet, at initial levels of introduction in high school it has been “described” as a set of “Mechanistic nature paths” that solve the problems without adequate justification. Far from this interpretation, some geometry treaties establish training pathways that simplify learning of this science.

The geometry (Latin geometry, which comes from the Greek language γεωμετρία, geo landmetria measure), is a branch of mathematics that deals with the study of the properties of geometric figures in the plane or space, like: points, straight, planes, polytopes (including parallel, perpendicular, curves, surfaces, polygons,polyhedra, etc.).(W)

In these pages two images are proposed summarizing a possible strategy or sequence gradually incorporating the basics of this branch of science in the education of our students.

At first the basics educational level would be set on which further developments will be supported:

  • Theorem of Thales
  • Pythagorean Theorem
  • Arco able
  • Power Concepts
  • Fundamental Problem Tangencies

Secuencia geométrica


Tras la incorporación de los conceptos básicos anteriores podemos avanzar en el estudio vertical de detalle de los conceptos básicos aprendidos. So, el concepto elemental de “power” nos permitirá acometer el “fundamental problem of tangents” en cualquiera de sus variantes, y la incorporación del concepto de “Beam circumferences” facilitará una generalización más amplia del mismo.Secuencia geométrica 2

Esta secuencia puede completarse posteriormente con el estudio clásico de los problemas de tangencias y el estudio métrico de las cónicas.

Metric geometry

Related Posts

  • Conic as Locus Centers Circumferences TangentsConic as Locus Centers Circumferences Tangents We have seen that the study of conic can be made from different geometric approaches. En particular, to start analyzing conic we have defined as the ellipse locus, we said that: Ellipse is the locus of points in a plane whose sum […]
  • Metric geometry : Investment beam circumferencesMetric 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" by various […]
  • Investment: Table mental gymnastics processing elementsInvestment: 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 […]
  • conic metric: Head circumferenceconic metric: Head circumference We have defined the ellipse as the "locus of centers circumferences, through a focus, They are tangent to the focal circumference of the other focus center". This definition allows us to approach the study of the conic by applying the concepts seen to […]
  • The robustness of dynamic geometric constructions with Geogebra: Polar of a point of a circleThe robustness of dynamic geometric constructions with Geogebra: Polar of a point of a circle The study of the disciplines of classical geometry can be reinforced by using tools that allow constructions that can be changed dynamically: variational constructions. The tool "Geogebra" It will serve to illustrate […]
  • Reversing a point. 10 constructions for obtaining [I- Metrics]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 […]