26 citations · 60 across the 12 of their papers we have counts for
12 papers
Construction of Gyrogroups of Order by Cyclic 2-Groups
Abraham A. Ungar, Mohammad Ali Salahshour, Kurosh Mavaddat Nezhaad
A gyrogroup is a structure constituting from a non-empty set and a binary operation such that satisfying the left identity, and left inverse conditions, and also has the associativ…
Bi-gyrogroup: The group-like structure induced by bi-decomposition of groups
Teerapong Suksumran, Abraham A. Ungar
The decomposition of a group into a subset and a subgroup of induces, under general conditions, a group-like structure for , known as a gyrogroup. The fam…
Parametric Realization of the Lorentz Transformation Group in Pseudo-Euclidean Spaces
Abraham A. Ungar
The Lorentz transformation group is a group of Lorentz transformations of order , that is, a group of special linear transformations in a pseudo-Euclidean space of…
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…