Open AccessPolygons in hyperbolic geometry using Beltrami-Klein models
Author(s) -
R Patmaningrum,
H P Lestari
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1581/1/012053
Subject(s) - polygon (computer graphics) , geometry , hyperbolic triangle , hyperbolic geometry , mathematics , klein–gordon equation , foundations of geometry , absolute geometry , ultraparallel theorem , point (geometry) , differential geometry , projective geometry , regular polygon , physics , convex set , telecommunications , convex optimization , frame (networking) , nonlinear system , quantum mechanics , computer science
Hyperbolic geometry was a geometry based on Hyperbolic Parallel Postulate. The purpose of this research was to describe the model of basic objects, concepts of triangles and polygons, as well explain types of polygons in hyperbolic geometry used the Beltrami-Klein model. The research method was literature study, it studied the definition and axiom were related to Euclid geometry and hyperbolic geometry such as point, line, triangle, and polygon. The result of this study was: 1) The plane model for Beltrami-Klein model is a γ circle. The object of geometry such as Klein points was expressed as a dot, Klein lines was expressed as part of Euclid lines that contained in a γ circle, Klein distances and Klein angles has the same presentation as Euclid distances and Euclid angles. 2) The Klein triangles have different concepts from the Euclid triangles. 3) The Klein polygons were defined as a combination of Klein segments, Klein rays, or Klein lines that was foreign to each other and have n different Klein points that was not collinearities. 4) The Klein polygons were divided into two types, the ordinary Klein polygons and the asymptotic Klein polygons.