To study the tangential Conic, and in particular the proyectividades between beams of second order superimposed on a same curve, We can rely on the dual study of the accomplished with overlapping series of second order.
The projective concepts that we have developed to study the overlapping series of second order, whose base is a conical, They allow to solve problems of determination of tangent points of a Conic defined by five points or five restrictions through the combination of points and tangents with their respective points of tangency.
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.
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.
When analyzed in what looks like a fern, the coast and a snowflake we see the concept of self-similarity appears recurrently, giving rise to geometric shapes based on the concepts of recursion. We have seen how a recursive fractal is generated, and we have even analyzed the Koch curve or triangle… (leer más)
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