Direcciones de Cavalieri entre dos triángulos

• Autores: Eugenio Roanes Macías
• Localización: Boletín de la Sociedad Puig Adam de profesores de matemáticas, ISSN 1135-0261, Nº. 92, 2012, págs. 30-50
• Idioma: español
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• Resumen

  • Although Cavalieri principles were set forth in the XVII century, they already appeared implicit in Archimede´s discoveries about areas and volumes. The application to triangles of the first principle admits a reciprocal theorem: any two triangles of the same area are always Cavalieri-congruent. This result was discovered and proved in 1988 and other proofs have appeared since them. In this article the problem is developed following several lines: 1) giving another solution based on a unique rotation; 2) determining the number of directions for the sheaf of parallel lines; 3) calculating such directions depending on the two triangles.