Determinación de lugares geométricos , vía sintética y computacional, aplicada a lugares de tipo cisoide

Resumen

An automatic method for determining geometric loci directly from its geometric construction is applied to obtain several loci of the type cissoid. This method uses, successively: a Dynamic Geometry System, to draw the geometric configuration with the mouse and to obtain a constructive geometric algorithm; an external translator ( developed by the authors), to convert the geometric algorithm into a Computer Algebra System (GAS) syntax; an Euclidean Geometry package ( denoted paramLoc, also developed by the authors), that allows the GAS to interpret the translated code and the capabilities of the GAS (to obtain the parametric and implicit equations of the locus and to plot the locus curve). The method is applied: to an original locus that lead to the usual cissoid curve; to a 1-parametric family of loci of the type cissoid; to the classic Newton's cissoid locus and to Diocles' cissoid locus. This type of loci was chosen because the standard difficulties that users of this automatic method can find, show up in these examples. Comparisons with classic methods that use techniques from Synthetic Geometry techniques are included.