Aplicação do teorema de Ptolomeu em teoria dos números

Abstract

Mathematics has an irresistible elegance and an essential utility in our lives. However, not rarely, simple mathematical problems require complex strategies for resolution. Then charm is taken by disappointment or by a persistent search for simple solutions that are not always found masterfully. The fact is that we can relate the techniques of a particular area in mathematics to problems in other areas, and this is what our work consists in. We will use some geometric results related to Ptolemy's theorem, in order to simplify the solutions of some problems in number theory. Number theory is a branch of mathematics that has its well-known particularities in the search for problem demonstrations that took years to solve, and others that have not come to any conclusion despite many scholars’ efforts. Some problems have not taken so many years to be solved, but their solutions were presented in a complex way. With the use of strategies of the geometry milieu even high school students are mature enough to understand what is being presented. If those problems were simply solved with arguments of the number theory, their understanding could become even more difficult for many under graduating students.