# 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

Origen de la projective geometry

Parallel lines intersect at infinity, Myth or Reality?

## projective

Fundamentals projective: Geometries

Categories projective geometric shapes and operations

Theorem of Thales

Ordered triples of elements

Elements arranged quaterns

Perspectivity

Dynamic construction of a quadruplet of points Geogebra

## Concepts of harmonic relations

Polar of a point with respect to two lines

## Projectivity in forms of first order

Projectivity

Overlapping shapes first order

What is an involution in geometry?

Projective projective axis of two series

Determination of homologous elements in series projective

projective axis of two series with Geogebra Interactive

Projective center of two projective bundles

Determination of homologous elements in projective beams

projective center of two interactive Beams with Geogebra

## Projectivity in second-order forms

Definition of the conical projective

Circumference as a series of second order

Intersection of straight and tapered

Tangent from a point to a conical

Overlapping series of second order

Application of overlapping series of second order

You do overlapping of second order

Application of second-order overlapping beams

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

## Involution in second-order series

Axis of involution

Autopolares triangles

Center of involution

Centro de la cónica

Conjugate directions

Conjugate polar diameters

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.