Geometria não euclediana e polígonos hiperbólicos via pyscript

Abstract

Since the times of Euclid (300 BC) until the 19th century, in an attempt to prove Euclid’s parallel postulate, new geometries emerged. An example of non-Euclidean geometry is hyperbolic geometry, which differs from Euclidean geometry only with respect to parallelism, stating that through a point not belonging to a line r, more than one parallel line passes through r. As a consequence, we have that the sum of the interior angles of a hyperbolic triangle is strictly less than 180 degrees. Another point that it not intuitive is the AAA case, that is, if two triangles have their three angles congruent respectively, then these triangles are congruent. In this work, a Web interface was also developed to draw lines in hyperbolic plane and calculate the measure of interior angles of any hyperbolic polygon using PyScript, a tool that allows users to create Python applications together with Javascript and HTML.