Building hyperbolic tessellations on the Poincaré disk with GeoGebra
DOI:
https://doi.org/10.23925/2237-9657.2022.v11i2p017-032Keywords:
Hyperbolic geometry, Works by Escher, Mathematics TeachingAbstract
We present in this work some characteristics of the Poincaré disk geometry, hyperbolic geometry in the plane, such as hyperbolic line, parallelism, distance between two points, hyperbolic polygons and circles, the sum of the internal angles and the area of a hyperbolic triangle. We associate some works by the Dutch graphic artist Maurits Cornelis Escher with tessellations on the circle, and we used GeoGebra’s hyperbolic tools to build two-dimensional figures and a tessellation with hyperbolic triangles on the Poincaré disk. We conclude that GeoGebra is a great app to be explored in the study of non-Euclidean geometries in the plane, especially in Mathematics-Teaching Degree Course.
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