An Introduction to Hyperbolic Barycentric Coordinates and their Applications

Barycentric coordinates are commonly used in Euclidean geometry. The adaptation of barycentric coordinates for use in hyperbolic geometry gives rise to hyperbolic barycentric coordinates, known as gyrobarycentric coordinates. The aim of this article is to present the road from Einstein's velocity addition law of relativistically admissible velocities to hyperbolic barycentric coordinates along with applications.Comment: 66 pages, 3 figure

Gyrations: The Missing Link Between Classical Mechanics with its Underlying Euclidean Geometry and Relativistic Mechanics with its Underlying Hyperbolic Geometry

Being neither commutative nor associative, Einstein velocity addition of relativistically admissible velocities gives rise to gyrations. Gyrations, in turn, measure the extent to which Einstein addition deviates from commutativity and from associativity. Gyrations are geometric automorphisms abstracted from the relativistic mechanical effect known as Thomas precession

Brief Note: A Significant Seed Bank for Spergularia marina (Caryophyllaceae)

Author Institution: Department of Botany, Ohio UniversityThe seed bank of Spergularia marina averaged 471,135 seeds m~2 in an Ohio salt marsh, representing the largest seed pool reported in the literature for a flowering plant community. Seed banks perform an important role in maintaining populations of annual halophytes, such as S. marina, in salt marshes, because of the local extinction of plant populations in these unpredictable and highly stressful saline environments

On algebraic endomorphisms of the Einstein gyrogroup

We describe the structure of all continuous algebraic endomorphisms of the open unit ball $\mathbf{B}$ of $\mathbb{R}^3$ equipped with the Einstein velocity addition. We show that any nonzero such transformation originates from an orthogonal linear transformation on $\mathbb{R}^3$