Rediscovering and extending sorne classic geometric loci with the help of GeoGebra

• Eugenio Roanes Macías ^[1] ; Eugenio Roanes Lozano ^[1]
  1. [1] Universidad Complutense de Madrid

     Universidad Complutense de Madrid

     Madrid, España

     
• Localización: Boletín de la Sociedad Puig Adam de profesores de matemáticas, ISSN 1135-0261, Nº. 112, 2021, págs. 7-26
• Idioma: inglés
• Títulos paralelos:
  • Redescubriendo y extendiendo algunos lugares geométricos clásicos con ayuda de GeoGebra
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• Resumen

  • An experimental method devoted to rediscover classical geometric loci and find new branches of the curve of the locus is proposed. It is executed on the Graphic Window of GeoGebra. It is compared with two classi-cal methods of loci determination, based on Synthetic Geometry and Elementary Analytical Geometry (using Cartesian coordinates), respec-tively. It is applied to three classic loci: a first locus consideri,ng "the difference of squares of distances to two fixed points being constant", a second locus derived from the "Altitude Theorem" and a third locus considering "the difference of squares of distances to two fixed points being constant", a second locus derived from the "Altitude Theorem". and a third locus derived from the "Leg Theorem". In the first one only the classical solution is obtained; in second one a new branch is rediscovered (which had already been previously found by other authors using a computer algebra method); and in the third one two new branches are obtained (first featured in this article, as far as we know). Finally, some reftections on the didactic interest of this method, in relation to the classical methods for studying geometric loci, as a prior or support method, are considered.