higher geometry / derived geometry
Ingredients
Concepts
geometric little (β,1)-toposes
geometric big (β,1)-toposes
Constructions
fundamental β-groupoid in a locally β-connected (β,1)-topos / of a locally β-connected (β,1)-topos
Examples
derived smooth geometry
Theorems
A polar coordinate system for Cartesian space is a coordinate system adapted to the decomposition of the complement of the origin as a Cartesian product of the unit n-sphere times the positive real numbers inside the real line:
If denotes the standard volume form on the unit n-sphere, then the standard volume form of Cartesian space in polar coordinates is
where denotes the canonical coordinate function along the radial direction.
If a smooth function depends at most on the radius coordinate and the angle of vectors in to any fixed line through the origin, then
sign correct?
See also
Wikipedia, Polar coordinate system
Wikipedia, Spherical coordinare system
Last revised on December 1, 2019 at 19:09:58. See the history of this page for a list of all contributions to it.