Reconstruyendo polígonos complejos a partir de los puntos medios de sus lados

Aledo, Juan A. ^[1] ; Calatayud, Julia ^[2] ; Cortés, Juan Carlos ^[2] ; Jornet, Marc ^[2]
1. [1] Universidad de Castilla-La Mancha
  
  Universidad de Castilla-La Mancha
  
  Ciudad Real, España
2. [2] Universidad Politécnica de Valencia
  
  Universidad Politécnica de Valencia
  
  Valencia, España
Localización: Boletín de la Sociedad Puig Adam de profesores de matemáticas, ISSN 1135-0261, Nº. 109, 2020, págs. 27-38
Idioma: español
Títulos paralelos:
- Recontructing complex polygons from the medium points of its sides
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Resumen
- In this paper we study the following problem. Let M1,...,Mn be >= 3 distinct points in the real plane R2. Under what conditions there exist points A1,...An E R2. such that Mi is the middle point of the segment AiAi+1 for i=1,...,n-1 and Mn is the middle point of the segment AnA1?We prove that the answer is generically in the affirmative, with uniqueness, if n is odd whereas in case n is even all possibilities can occur, that is, either there is no solution, or there exists a unique one, or there exist infinitely many ones.