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19 de may. de 2024 · For any surface embedded in Euclidean space of dimension 3 or higher, it is possible to measure the length of a curve on the surface, the angle between two curves and the area of a region on the surface. This structure is encoded infinitesimally in a Riemannian metric on the surface through line elements and area elements.
Hace 2 días · The preferred inertial motions are related to the geometry of space and time: in the standard reference frames of classical mechanics, objects in free motion move along straight lines at constant speed. In modern parlance, their paths are geodesics, straight world lines in curved spacetime.
Hace 1 día · Howard talks about curved space
Hace 5 días · First, we define a novel spin supplementary condition for the electromagnetic interactions which generalizes the one proposed by Ohashi-Kyrian-Semerák for gravity. As a result, we get the whole family of charged spinning particle models in the curved spacetime with remarkably simple dynamics (momentum and velocity are parallel).
Hace 2 días · A proper reference frame in the theory of relativity is a particular form of accelerated reference frame, that is, a reference frame in which an accelerated observer can be considered as being at rest. It can describe phenomena in curved spacetime, as well as in "flat" Minkowski spacetime in which the spacetime curvature caused by ...
Hace 4 días · Derivatives can be used to obtain vectors tangent to and perpendicular to given curves and surfaces. Specifically: The gradient operator – ∇ = (∂/∂ x , ∂/∂ y) in 2D, or ∇ = (∂/∂ x , ∂/∂ y, ∂/∂ z) in 3D – can be used to obtain vectors perpendicular to curves and surfaces represented with implicit algebraic equations.
Hace 5 días · While it may be challenging to comprehend the curvature of space, it can be imagined as a two-dimensional plane that has the potential to be curved into different shapes – a sphere, a saddle, or a flat surface. In each case, the curvature of space would be either positive, negative, or flat, respectively.
