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Metric Geometry

The study of the different geometries (Metrics, descriptive, projective) starts at the bachelor but finds its most abstract to the university levels.

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)

These pages present a set of structured basics that allow a reasoned initiate us in beautiful study of this discipline, geometry, basis of understanding in mechanical engineering designs.

Metric Geometry

geometriaThe metric geometry is applied in Euclidean space is based on the theorems of Thales and Pythagoras.

The notions of the relationship between central and inscribed angles in a circle round the basics of learning to understand the Metric Geometry.

The lesson plans presented sequentially the set of concepts underlying geometric constructions. Add basic exercises that strengthen and settle these concepts.

All PPT files are in PowerPoint format

Preliminary Concepts (CP): Study of some theorems and elementary properties of classical geometry.

 

Learning Path Metric Geometry

Learning Path Metric Geometry

 

Basic concepts in metric geometry

Nociones sobre ángulos

Notions of angles

Thales de Mileto : Teorema de Thales

Theorem of Thales

Pitágoras

Pythagorean Theorem

Equation of the circle

Equation of the circle

Ángulos en la circunferencia : Central e inscrito

Angles on the circumference : Central and inscribed

Arco capaz sobre un segmento

Arco able on a segment

Arco able on a segment : Example [I]

Arco able on a segment : Example [I]

Arco able on a segment : Solución [I]

Arco able on a segment : Solución [I]

Arco able : Problema II

Arco able : Problema II

Arco able : Problema II Solución

Arco able : Problema II Solución

Potency to a circumference

Potencia de un punto respecto de una circunferencia

Potencia de un punto respecto de una circunferencia

Generalización del concepto de “Potencia”

Generalization of the concept of "Power"

Triangle geometry

Teoremas de la altura y del cateto

Theorems height and leg

Triangle geometry: Problem 1

Triangle geometry: Problem 1

loci of interest

Difference of squares of distances from two fixed points

Difference of squares of distances from two fixed points

Geometric transformations

Transformaciones geométricas : Homografías Vs Correlaciones

Geometric transformations : Correlations Vs homographies

Homotecia

Homotecia

Inversión en el plano

Investment in the plane

Reversing a point (Metrics)

Reversing a point (Metrics)

Inversion table

Inversion table

The problem of the spin Center

The problem of the spin Center

Equivalence

Square equivalent

Square equivalent

Fundamental Problem Tangencies (PFT)

Problema fundamental de tangencias : PPr

Problema fundamental de tangencias : PPr

The problem with football

The problem with football

Problema fundamental de tangencias : PPc

Problema fundamental de tangencias : PPc

Determinación de rectas con condiciones angulares

Determination of lines with angular conditions

Determinación de circunferencias de radio conocido con condiciones angulares

Determining radio circumferences known angular conditions

Inversión : Aplicación a la resolución de problemas de tangencias y angulares

Investment : Application to the resolution of problems and angular tangents

Apollonius and his ten problems

Apollonius and his ten problems

Problem of Apollonius : rcc

Problem of Apollonius : rcc

Problem of Apollonius : ccc

Problem of Apollonius : ccc

Corradicales circumferences Beams

Suma/Diferencia de cuadrados de distancias a dos puntos fijos

Sum / Difference of squares of distances from two fixed points

Eje radical

Radical Axis

Getting Radical Axis

Getting Radical Axis

Corradicales circumferences Beams

Corradicales circumferences Beams

Make circles parabolic

Make circles parabolic

Haz elíptico de circunferencias

Haz elíptico de circunferencias

Make hyperbolic circles

Make hyperbolic circles

Generalization of the fundamental problem of tangents

Generalization of the fundamental problem of tangents

Investment beam circumferences

Investment beam circumferences

Polar of a point P with respect to a circumference c Geogebra

Polar of a point P with respect to a circumference c Geogebra

Problems

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

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

Conical

Conical

Conical

Ellipse as locus

Ellipse as locus

Conic as Locus circumferences Tangents

Conic as Locus circumferences Tangents

conic metric: Head circumference

conic metric: Head circumference

Conical defined by the two foci and a point

Conical defined by the two foci and a point

Conical defined by the two foci and a tangent

Conical defined by the two foci and a tangent

Problems

Loci

Selectivity 2014 – B1

Selectivity 2014 – B1

Solución Selectividad 2014 – B1

Solución Selectividad 2014 – B1

Angularidad Básica

Circunferencias con condiciones angulares

Circunferencias con condiciones angulares

Solución

Solución

The problem with the pool table

The problem with the pool table

The problem with the pool table: Solución

The problem with the pool table: Solución

The problem of the two peoples and the bridge

The problem of the two peoples and the bridge

The problem with football

The problem with football

Determinación de un segmento conocido su punto medio

Determinación de un segmento conocido su punto medio

Determinación de un segmento conocido su punto medio [Solución]

Determinación de un segmento conocido su punto medio [Solución]

Enlace a Temas de Geometría Métrica elaborados for mis alumnos

Basics

Corradicalidad

  • LO-F-010. CP4-Power (CP_v14c4). Potencia de un punto respecto de una circunferencia. Training.
  • LO-F-011. CP5-Eje Radical (CP_v14c5). Radical axis of two circles. Centro radical. Training.

Transformaciones

  • LO-F-012. CP6-Equivalencia (CP_v14c6). Teoria y ejercicios.
  • LO-F-013. CP7-Transformaciones (CP_v14c7). Teoria y ejercicios.

Complementos

  • LO-F-014. CP8-Complementos (CP_v14c8). Complementos de Geometria.

Repaso acumulado

  • LO-F-015. Construccion de Formas poligonales (apuntes_4001_formasPoligonales.PDF). Poligonos Apuntes y del Profesor de Triangulos Victorino Gonzalez García editados en la Sección de publicaciones de la EUITA. (UPM).
  • LO-F-016. Preliminary Concepts (PDF). Apuntes del Profesor de Conocimientos preliminares Victorino Gonzalez García editados en la Sección de publicaciones de la EUITA. (UPM).

 

Power Concepts : Prezi

Power Concepts : Prezi