2017-05-302017-05-302014-06-27SILVA, Everaldo Raiol da. O surgimento das trigonometrias em diferentes culturas e as relações estabelecidas entre elas. 2014. 210 f. Dissertação (Mestrado) - Universidade Federal do Pará, Instituto de Educação Matemática e Científica, Belém, 2014. Programa de Pós-Graduação em Educação em Ciências e Matemáticas.https://repositorio.ufpa.br/handle/2011/8551The present study deals with the history of the plane and spherical trigonometry, with the central proposal emerged understand how the trigonometry's in different civilizations which are: Egyptian, Babylonian, Greek, Hindu, Arabic and Chinese. Our goal was to identify how trigonometry's emerged in which different civilizations and the relations between them. To achieve this goal, we divided the research into three phases. In the first phase of the study, we adopt as a methodological approach to literature, the history of mathematics and science, based on historical research into the development of flat and spherical trigonometry's. Among the theoretical frameworks with which we work are: Marconi (1986, 2007), Gil (1991, 1999), Lakatos & Martins (2005), and Miguel Miorim (2002, 2011), Valente (2007), D Ambrosio (2007) and Valdés (2012). In the second phase of the study in order to enhance the appearance and the evolution and development of the conceptual plane and spherical trigonometry in different civilizations which are: Egyptian, Babylonian, Greek, Hindu, Arabic and Chinese in antiquity through the Middle Ages and until the Renaissance period with the aid of mathematical history. For this, we use as theoretical Ronan (1987), Wussing (1998), Morey (2001, 2003), Cajori (2007), Mendes (2009), Pereira (2010, 2013), Katz (2010), Rooney (2012 ), Rosa (2012), Brummelen (2009, 2013), Flood and Wilson (2013), among others. In the third phase of the study made a historical study of geometry and non-Euclidean geometries, we observed for the appearance of spherical geometry and its implication with spherical trigonometry and show how relationships exist between flat and spherical trigonometry's, for this we use the method of series Taylor, our main objective of the study, both for use as theoretical: Ayres Jr. (1954), Hogben (1970), Do Carmo (1987), Wussing (1998), Imre Toth (2011), Brummelen (2009, 2013), among others. As conclusion of the study, we show how the trigonometry's in different civilizations and the relations between them arose, thus answering our research question, and also ways to let other researchers conduct further research as a result of the presentation and defense of the dissertation.Acesso AbertoMatemáticaTrigonometriaTrigonometria planaTrigonometria esféricaGeometriaHistória da matemáticaEducação em matemáticaHistória da trigonometriaDissertaçãoCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA