An algebraic approach to finding the Fermat¿Torricelli point

• Autores: Óscar Luis Palacios Vélez, J.A. Pedraza Oropeza, Villagran Escobar
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 46, Nº. 8, 2015, págs. 1252-1259
• Idioma: inglés
• DOI: 10.1080/0020739x.2015.1036947
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• Resumen

  • Using a calculus and an algebraic approach, the Cartesian coordinates of the Fermat–Torricelli point are deduced for triangles with no internal angle greater than 120°. Although in theory, the deduction of these coordinates could be made ‘by hand’, in practice it is very laborious to obtain them without the aid of mathematical computer software, but with human guidance, since there are mathematical artifices not yet incorporated into the software. It is also shown that these coordinates can be conveniently expressed in terms of the side lengths and the area of the triangle. These coordinates are contrasted with the coordinates of a similar point: one whose sum of the squares of the distances to the vertices of an arbitrary triangle is a minimum