Putra Pratama, Febriyana
*Konsistensi Aksioma-Aksioma Terhadap Istilah-Istilah Takterdefinisi Geometri Hiperbolik Pada Model Piringan Poincare.*
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## Abstract

This research aims to know the interpretation the undefined terms on Hyperbolic geometry and it’s consistence with

respect to own axioms of Poincare disk model. This research is a literature study that discusses about Hyperbolic

geometry. This study refers to books of Foundation of Geometry second edition by Gerard A. Venema (2012),

Euclidean and Non Euclidean Geometry (Development and History) by Greenberg (1994), Geometry : Euclid and

Beyond by Hartshorne (2000) and Euclidean Geometry: A First Course by M. Solomonovich (2010). The steps taken

in the study are: (1) reviewing the various references on the topic of Hyperbolic geometry. (2) representing the

definitions and theorems on which the Hyperbolic geometry is based. (3) prepare all materials that have been

collected in coherence to facilitate the reader in understanding it. This research succeeded in interpret the

undefined terms of Hyperbolic geometry on Poincare disk model. The point is coincide point in the Euclid on circle

. Then the point onl γ is not an Euclid point. That point interprets the point on infinity. Lines are categoried in two

types. The first type is any open diameters of . The second type is any open arcs of circle. Half-plane in Poincare

disk model is formed by Poincare line which divides Poincare field into two parts. The angle in this model is

interpreted the same as the angle in Euclid geometry. The distance is interpreted in Poincare disk model defined by

the cross-ratio as follows. The definition of distance from to is , where is

cross-ratio defined by ̅̅̅̅ ̅̅̅̅ ̅̅̅̅ ̅̅̅̅ . Finally the study also is able to show that axioms of

Hyperbolic geometry on the Poincare disk model consistent with respect to associated undefined terms

Item Type: | Artikel Dosen |
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Subjects: | Q Science > QA Mathematics |

Divisi / Prodi: | Faculty of Applied Science and Technology (Fakultas Sains Dan Teknologi Terapan) > S1-Mathematics (S1-Matematika) |

Depositing User: | Dr. Julan Hernadi |

Date Deposited: | 04 Jan 2023 02:52 |

Last Modified: | 04 Jan 2023 02:52 |

URI: | http://eprints.uad.ac.id/id/eprint/38403 |

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