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Categories Projectivity

Geometría proyectiva: Determination of homologous elements in series projective

One of the first problems we must learn to work in projective geometry is the determination of homologous elements. To start the study will use the methodology to be used as usual model-based elements “points”, since it is easier to interpret. Therefore we will consider the determination of homologous elements in series projective:
Given two projective series defined by three pairs of elements (points) counterparts, determine the counterpart of a given point.

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Geometría proyectiva: Definition of the conical projective

Conic curves, further treatment of the metric based on the notions of tangency, have a projective treatment that relies on the concepts of sets and projective bundles.

We will see two definitions of conic adapted to “World points” o al “world of straight” according to the interest, in what is defined as the definitions “point” or “tangential” of conic curves.

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Geometría proyectiva: Projective center of two projective bundles

Using the laws of duality in projective models can get a set of properties and dual theorems from other previously deducted. Obtaining homologous elements in the projective case series was performed by obtaining intermediate pespectividades allowed perspectival do we get what we have called “projective axis”. We will see that in the case of projective bundles, Dual reasoning leads us to determine projective centers.

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Geometría proyectiva: Projective projective axis of two series

The operational prospects relationships is reduced to the concepts of belonging, so we will use these techniques to suit projective models simplify obtaining homologous elements.
How can we define two projective series? On how many homologous elements are necessary to determine a projectivity?How can we obtain homologous elements?

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