# Geometría proyectiva: Dynamic construction of a Tetrad of points [Geogebra]

Application “Geogebra” It allows you to develop dynamic constructions in which we can modify the position of the elements forming it, keeping the geometric constraints of these figures, allowing the invariants of the same show. This tool can be a valuable aid for students.

Professor Juan Alonso Alriols collaborated in the introduction of this tool in the teachings of “Graphic Expression” at the Polytechnic University of Madrid, providing examples of high interest. You can see an example of his work in the “Dynamic construction of double reason for four points” accompanying this entry, that has added a driver text for use in our classes.

# Geometría proyectiva: Construction of quadruples of points

We have seen the definition of ordered quadruples of elements, characterizing rectilinear some four points or four straight from a bundle of planes through a value or characteristic, result for the ratio of two triads determined by such elements.

We then consider the problem of obtaining, given three elements belonging to a same form of first category, series or beam, get a fourth element that determines a Tetrad of particular value.

# Geometría proyectiva: Perspectivity

Projective foundations are based on the definitions of "ordered triples of elements" and “quaternions for defining the cross ratio”, and relationships called “perspectives” between elements of identical or different nature.
These perspectives relations, that will be used in determining projections representation systems, defined from two projective operators:
Projection
Section

# Geometría proyectiva: Elements arranged quaterns

Analogously to the definition of saw “ordered triples of elements”, we can state a definition that involves four elements.

The non-conservation of the simple reason conical projections necessary to study a new model that is applicable in these representations, a new invariant present in double reasons.