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

Juan Angel Aledo Sánchez , Julia Calatayud, Juan Carlos Cortés López , Marc Jornet Sanz

• 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.