Números p-ádicos e o teorema de Monsky

Abstract

Monsky's theorem states that a square cannot be divided into an odd number of triangles of equal area. In the present work we present the demonstration of this fact, as well as the concepts and results necessary to understand it. The Introduction contains the historical context and some attempts to prove the theorem. In chapters two and three we see two important results used in the proof: Sperner's Lemma and Chevalley's Theorem. Chapter three also contains the construction of the body of p-adic numbers and some of their properties. In chapter four we have the proof of Monsky's Theorem and we discuss possible generalizations and open problems.