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

Emergency Tenant Protection in New York: Ten Years of Rent Stabilization

New York City\u27s rent stabilization system was designed as an alternative to the rent control system. Rent stabilization looked to the owners for supervision as a way to benefit not only the system but tenants through an informed and experienced administration. Unfortunately, the system has had its fair share of shortcomings as rules have become technical, complex, and ill equipped to address the concerns of tenants. This comment examines the stabilization system\u27s history and its current status. Though the current system has flaws, the flaws can be fixed and must be to protect NYC tenants and owners

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