Flat (geometry) - Wikipedia
In geometry, a flat is an affine subspace, i.e. a subset of an affine space that is itself an affine space. [1] Particularly, in the case the parent space is Euclidean, a flat is a Euclidean …
Minkowski space - Wikipedia
In physics, Minkowski space (or Minkowski spacetime) (/ mɪŋˈkɔːfski, - ˈkɒf -/ [1]) is the main mathematical description of spacetime in the absence of gravitation. It combines inertial space …
general relativity - Why is Spacetime described as flat even …
2023年8月23日 · "Flat space" means that on large scales, Euclidean geometry holds. All the angles in any triangle drawn in space add up to 180°; the total distance between points …
42 Curved Space - The Feynman Lectures on Physics
The analog of a straight line in space is for space-time a motion at uniform velocity in a constant direction. The curve of shortest distance in space corresponds in space-time not to the path of …
The Universe Is Flat — Now What? | Space
2016年12月7日 · You heard it here first: Cylinders are flat. There's an important distinction between geometry, the behavior of parallel lines, and topology, the way a space can get all …
Lecture Notes on General Relativity - S. Carroll
In flat space in Cartesian coordinates, the partial derivative operator is a map from (k, l ) tensor fields to (k, l + 1) tensor fields, which acts linearly on its arguments and obeys the Leibniz rule …
To endow three-dimensional space with geometry, we can specify a line ele-ment. The line element assigns a length L(P) to every nite path P. For at space, the line element de nes a …
Why is Minkowski spacetime in polar coordinates treated in texts …
Taking 3-D Minkowski spacetime line element in General Relativity: ds2 = −c2dt2 + dx2 + dy2 + dz2, d s 2 = − c 2 d t 2 + d x 2 + d y 2 + d z 2, when considering a change into spherical …
Geodesics: Straightest or Shortest? When and Why?
2017年7月4日 · You're asking for a "deep reason" why in flat space the shortest distance between two points is a straight line. I don't think there's a "deeper" reason for this than for the fact that …
The linear-space structure of V embodies more information than its flat-space structure. As a linear space, V has a distinguished element, 0, but as a flat space it is homogeneous in the …