26 citations · 60 across the 12 of their papers we have counts for
7 papers · 1 filter
On the Study of Hyperbolic Triangles and Circles by Hyperbolic Barycentric Coordinates in Relativistic Hyperbolic Geometry
Abraham A. Ungar
Barycentric coordinates are commonly used in Euclidean geometry. Following the adaptation of barycentric coordinates for use in hyperbolic geometry in recently published books on a…
An Introduction to Hyperbolic Barycentric Coordinates and their Applications
Abraham Albert Ungar
Barycentric coordinates are commonly used in Euclidean geometry. The adaptation of barycentric coordinates for use in hyperbolic geometry gives rise to hyperbolic barycentric coord…
Möbius Transformation and Einsten Velocity Addition in the Hyperbolic Geometry of Bolyai and Lobachevsky
Abraham A. Ungar
In this chapter, dedicated to the 60th Anniversary of Themistocles M. Rassias, Möbius transformation and Einstein velocity addition meet in the hyperbolic geometry of Bolyai and Lo…
Gyrogroups, the Grouplike Loops in the Service of Hyperbolic Geometry and Einstein's Special Theory of Relativity
Abraham A. Ungar
In this era of an increased interest in loop theory, the Einstein velocity addition law has fresh resonance. One of the most fascinating aspects of recent work in Einstein's specia…
Einstein's Special Relativity: The Hyperbolic Geometric Viewpoint
Abraham A. Ungar
The analytic hyperbolic geometric viewpoint of Einstein's special theory of relativity is presented.
Gyrations: The Missing Link Between Classical Mechanics with its Underlying Euclidean Geometry and Relativistic Mechanics with its Underlying Hyperbolic Geometry
Abraham A. Ungar
Being neither commutative nor associative, Einstein velocity addition of relativistically admissible velocities gives rise to gyrations. Gyrations, in turn, measure the extent to w…