A Mathematical Approach to the Plato's Problem
  Maybe the first inverse problem presented in the history of the occidental thought is described in the book Republic, written by Plato. The problem is posed in the Book VII in a text known as the Allegory of the Cave. That text motivated us to formulate a simple mathematical model that simulates, in a sense, the situation of the persons described in that problem. 
Luiz Bevilacqua, Adilson J. V. Brandao and Rodney Bassanezi