Graphic PIZiadas

Graphic PIZiadas

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Categories Polarity

Geometría proyectiva: Obtaining conical shafts from two pairs Diameters Polar Conjugates

A conical axes are those conjugates polar diameters are orthogonal to each.

We recall that two polar conjugate diameters, necessarily pass through the center O of the conical, are the polar two points unfit (located at infinity) that they are conjugated, namely, the polar of each of these points contains the other.

These pairs of elements determine an involution of diameters (polar) Conjugates will be defined when two pairs of beams know and their homologues.

Geometría proyectiva: Conjugate polar diameters

We have seen the definition of polar conjugate diameters, given to analyze the concept of Conjugate directions:

Conjugate polar diameters: They are polar two conjugated improper point.
Let's see how we can relate this concept with the triangle's autopolar seen in Involutions in second-order series.

Polar of a point with respect to two lines

The concept of polarity is linked to the harmonic separation.

This concept is Basic for the determination of the fundamental elements of conics, as its Center, conjugate diameters, axes ….

It will allow to establish new transformations which include homographies and correlations of great importance.