2017-03-202016-12-09CARVALHO, W. S. Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra. 2016. 52 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2016.http://repositorio.bc.ufg.br/tede/handle/tede/6970In this dissertation, we first state Euler's polyhedral formula for a set of points with Euler characteristic 2. We address the two known ways to prove Euler's Theorem: beginning with the classical proof by using Euclidian Geometry and afterwards we take the advantage of Spherical Geometry to give another proof. Furthermore, we address a version of Euler's formula for planar polyhedron, as well as, Pick's formula and the equivalence between Euler and Pick's formula. In the end, we provide application of Euler and Pick's formula, via two pedagogy tools Geoplano and GeoGebra, by giving examples to teach in classroom.application/pdfAcesso AbertoFórmula de eulerFórmula de pickGeoplanoGeoGebraEuler's theoremPick's theoremGeoplanGeoGebraCIENCIAS EXATAS E DA TERRA::MATEMATICADissertação