2,814 research outputs found
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 of equipped with the Einstein
velocity addition. We show that any nonzero such transformation originates from
an orthogonal linear transformation on
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