Graphic PIZiadas

Graphic PIZiadas

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Projective Geometry

The projective geometry or “of false position” is the basis for the future study of systems of representation, where prospects relationships established application models. Sin embargo, This geometry can also be used to abstract reasoning as applies the metric geometry, being particularly useful in the study of curves and surfaces such as conic and quadric.

Introduction

Orígen de la geometría proyectiva

Origen de la projective geometry

Parallel lines intersect at infinity, Myth or Reality?

Parallel lines intersect at infinity, Myth or Reality?

Geometric elements and relationships

projective

Elementos geométricos

Fundamentals projective: Geometries

Categorías de las formas geométricas y operaciones proyectivas

Categories projective geometric shapes and operations

Teorema de Thales

Theorem of Thales

Ternas ordenadas de elementos

Ordered triples of elements

Elements arranged quaterns

Elements arranged quaterns

Perspectivity

Perspectivity

Construction of quadruples of points

Construction of quadruples of points

Dynamic construction of a quadruplet of points Geogebra

Dynamic construction of a quadruplet of points Geogebra

 

Concepts of harmonic relations

Full Cuadrivertice

Full Cuadrivertice

Polar of a point with respect to two lines

Polar of a point with respect to two lines

Projectivity in forms of first order

Projectivity

Projectivity

Overlapping shapes notch

Overlapping shapes first order

What is an involution in geometry?

What is an involution in geometry?

Projective projective axis of two series

Projective projective axis of two series

Determination of homologous elements in series projective

Determination of homologous elements in series projective

projective axis of two series with Geogebra Interactive

projective axis of two series with Geogebra Interactive

Projective center of two projective bundles

Projective center of two projective bundles

Determination of homologous elements in projective beams

Determination of homologous elements in projective beams

projective center of two interactive Beams with Geogebra

projective center of two interactive Beams with Geogebra

Projectivity in second-order forms

Definition of the conical projective

Definition of the conical projective

Circumference as a series of second order

Circumference as a series of second order

Intersection of straight and tapered

Intersection of straight and tapered

Tangent from a point to a conical

Tangent from a point to a conical

Overlapping series of second order

Overlapping series of second order

Application of overlapping series of second order

Application of overlapping series of second order

You do overlapping of second order

You do overlapping of second order

Application of second-order overlapping beams

Application of second-order overlapping beams

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

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

Involution in second-order series

Axis of involution

Axis of involution

Autopolares triangles

Autopolares triangles

Center of involution

Center of involution

Centro de la cónica

Centro de la cónica

Conjugate directions

Conjugate directions

Conjugate polar diameters

Conjugate polar diameters

polar axes of a conic from two pairs Diameters Polar Conjugates

polar axes of a conic from two pairs Diameters Polar Conjugates

  • LO-F-017. Projective FP1-Basics (FP_v09c1).
    Fundamentals projective. Projection Operations section. Ordered triples of elements.
    Training.
  • LO-F-018. FP2-quaternions (FP_v09c2).
    Element quaterns: Reason double.
    Training.
  • LO-F-019. FP3-perspectivity (FP_v09c3).
    Projective perspective.
    Training.
  • LO-F-020. FP4-Harmonic Relations (FP_v09c4).
    Foreign harmonic lines and circles orthogonal.
    Training.
  • LO-F-021. FP5-Projectivity (FP_v09c5).
    General projective. Axles and projective centers.
    Training.

Second order

  • LO-F-022. FP6-second order (FP_v09c6).
    Forms of second order. Conical.
    Training.
  • LO-F-023. FP7-Overlapping Forms (FP_v09c7).
    Projective shapes superimposed.
    Training.
  • LO-F-024. FP8-Involutions (FP_v09c8).
    Projective Involutions.
    Training.