# Representation Systems

Sistemas_de_representacion

# Fundamentos Proyectivos

Fundamentos Proyectivos (FP)

Representation systems are based on the operations or projective transformations.

Projective invariant concepts are analogous to the corresponding metric, constituting a geometry in which the measure leads to the form. The simple reason and the cross-ratio are in the conceptual basis of this model.

 Classification Representation Systems
 Fundamentals projective: Geometries Categories projective geometric shapes and operations Theorem of Thales Ordered triples of elements Projections Foreign prospects

### Diédrico System: Topología básica

 Fundamentals del System dihedral Projection of the line Third straight projection True magnitude of the line Projection of the plane Projection of points in the plane Incidence (Intersections) Intersections in outlook: straight and cuboids

### System dihedral: Paralelismo y perpendicularidad

 Theorem of the three perpendicular Straight lines in a plane parallel to the projection Fall line Perpendicular to a plane Distance from a point to a plane Distance from a point to a line

### System dihedral: Proyecciones auxiliares

 Fundamentals of auxiliary projections, changes in plane
 The problem of the CAP with three forms

• 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 (CP_v14c5).
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.

# Representation Systems

## Basics

• LO-F-025. SR1-Projections (SR_v15c1).
Fundamentals cylindrical and conical Screenings.
Training.
• LO-F-026. SR2-Projection Plans (SR_v15c2).
Projections on different planes. Projective Invariant.
Training.
• LO-F-027. SR3-Classification (SR_v15c3).
Classification of cylindrical and conical systems.
Training.

## Membership or incidence

• LO-F-028. SR4-Membership (SR_v15c4).
Membership and correspondence between elements projections.
Training.
• LO-F-029. SR5-Parallelism (SR_v15c5).
Conservation parallelism and obtaining cylindrical projections in the conical limit points.
Training.
• LO-F-030. SR6-Projection of planes (SR_v15c6).
Treatment of planes projections.
Training.
• LO-F-031. SR7-Incidence (SR_v15c7).
Treatment of intersections between lines and planes.
Training.

## Measure

Perpendicularity.
Training.
• LO-F-033. SR9-Measure (SR_v15c9).
Treatment distance measurement and.
Training.
• LO-F-034. SR10-auxiliary projections (SR_v15c10).
Projections auxiliary projection planes changes.
Training.
• LO-F-035. SR11-Turns and discouragements (SR_v15c11).
Money and dejection as auxiliary transformations to obtain real magnitudes.
Training.