Abstract

A unique hyperbolic geometry paradigm requires altering the Relativistic principle that absolute velocity is unmeasurable. There is no absolute velocity, but in the case where a constant velocity is made from a half-angle velocity, a variable velocity is the same as (absolute) acceleration. Relativity is based on local Lorentz geometry. Our mathematical geometry constructs circle and hyperbola vectors with hyperbolic terms in an original formulation of complex numbers. We use a point on a hyperbola as a frame of reference. A theory is given that time and our velocity are inversely related. The physical laws of motion by Galileo, Newton and Einstein are forged using the half-angle velocity to electromagnetic velocity. The field of kinetic, potential and gravitational force accelerations is established. An experiment exemplifies the math from the Earth’s frame of reference. We discover a possible dark energy and gravitational accelerations and a geometry of gravitational collapse.

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