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# Introdução ao Plano Hiperbólico com o Geogebra

Author: Claudia Maia | Afiliation: ESE-IPP |

Author: Lucile Vandembroucq | Afiliation: Universidade do Minho |

**Abstract:**The Hyperbolic Geometry is a geometry in which the famous parallel postulate of Euclidean geometry is not valid. In the hyperbolic plane, through a point outside a line, there exist at least two lines parallel to the given line. This geometry is recognized as the first example of a non-Euclidean geometry and was independently founded by the mathematicians Gauss, Lobachevsky and Bolyai. Models were subsequently developed by Beltrami, Klein and Poincare. In this paper we present the model called Poincaré Disk and present constructions in Geogebra in this model, in particular, the construction of a tessellation by regular polygons.

**Keywords:**Poincaré Disk, hyperbolic tesselations.

# Introdução ao Plano Hiperbólico com o Geogebra

Author: Claudia Maia | Afiliation: ESE-IPP |

Author: Lucile Vandembroucq | Afiliation: Universidade do Minho |

References

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Coxeter, H. M. (2003). The Trigonometry of Escher’s Woodcut Circle Limit III. *Mathematical Intelligencer*, 18(4), 42-46.

Iversen, B. (1992). *Hyperbolic geometry*. Cambridge: Cambridge university press..

Stillwell, J. (1996) *Sources of hyperbolic geometry*. History of Mathematics, n.º10. American Mathematical Society, Providence, RI; London Mathematical Society, London.