Del Teorema de Viviani, del Principio de Reflexión y de otros hitos camino del punto de Fermat

• Autores: Francisco J. Baena
• Localización: Boletín de la Sociedad Puig Adam de profesores de matemáticas, ISSN 1135-0261, Nº. 97, 2014 (Ejemplar dedicado a: Profesor Julio Fernández Biarge), págs. 63-83
• Idioma: español
• Texto completo no disponible (Saber más ...)
• Resumen

  • This paper attempts to relieve the shortage of texts dealing with the issue of Fermat´s point of a triangle and, more precisely, the difficuly to find in most of them a complete solution to the problem of the existence, uniqueness and position of Fermat´s point for an arbitrary triangle, without restricting ourselves to those whose angles are less than 120º. Two complete solutions of Fermat´s point problem are offered in this paper. The first one is based on Infinitesimal Calculus and the second one, of an entirely geometric character, relies on two results which have their own interest: a generalized Reflection Principle, in which the reflecion axis is notm a straight line but a circle, and a generalization of Viviani´s Theorem. The paper finishes with one construction of the Fermat´s point of a triangle using a ruler and a compass.