The Jagged Boundary-Edge Problem

• Autores: Antonio R. Quesada, Andrew Cooper, Laurie Dunlap
• Localización: Boletín de la Sociedad Puig Adam de profesores de matemáticas, ISSN 1135-0261, Nº. 89, 2011, págs. 14-33
• Idioma: inglés
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• Resumen

  • Suppose that a plot of land bounded between two parallel lines is separed into two subregions by a jagged-edge (polygonal arc). We answer the following question: Can we find a line segment of minimal length (whose endpoints are a function of the polygonal arc´s vertices), with one endpoint on each of the parallel lines, that separates the land into two subregions that have the same areas as the original subregions? We show the existence of a point, which is determined geometrically and algebraically via recursion, so that any segment between the boundaries that passes through this point, is a solution.