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Full-Text Articles in Physical Sciences and Mathematics
The Euler Line In Non-Euclidean Geometry, Elena Strzheletska
The Euler Line In Non-Euclidean Geometry, Elena Strzheletska
Theses Digitization Project
The main purpose of this thesis is to explore the conditions of the existence and properties of the Euler line of a triangle in the hyperbolic plane. Poincaré's conformal disk model and Hermitian matrices were used in the analysis.ʹ
Hyperbolic Transformations On Cubics In H², Frank S. Marfai
Hyperbolic Transformations On Cubics In H², Frank S. Marfai
Theses Digitization Project
The purpose of this thesis is to study the effects of hyperbolic transformations on the cubic that is determined by locus of centroids of the equilateral triangles in H² whose base coincides with the line y=0, and whose common vertex is at the origin. The derivation of the formulas within this work are based on the Poincaré disk model of H², where H² is understood to mean the hyperbolic plane. The thesis explores the properties of both the untransformed cubic (the original locus of centroids) and the transformed cubic (the original cubic taken under a linear fractional transformation).