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On a sphere, the sum of the angles of a triangle is not equal to 180°. A sphere is not a Euclidean space, but locally the laws of the Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is very |
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There are 5 summaries on Manifold.
Encyclopedia and Summary Information
summary from source:
 Manifold Summary
990 words, approx. 3 pages
 A manifold is a curve, surface, or higher-dimensional space that has, at every point in that space, a small neighborhood around each point that looks like a ball in the corresponding Euclidean space of the appropriate dimension. More precisely, the... summary from source:
 Manifold Summary
64 words, approx. 0 pages
In mathematics, a topological space (&see; topology) with a family of local coordinate systems related to each other by certain classes of coordinate transformations. Manifolds occur in algebraic geometry, differential equations, and classical... summary from source:
 Manifold Summary
42 words, approx. 0 pages
. A variegated complex of elements considered as it is before being organized. For Kant especially, the sensory manifold is the as yet unstructured variety of material presented to the senses, which the mind then organizes through concepts, so that... summary from source:
Manifold Summary
19 words, approx. 0 pages
A pipe or chamber attached to several separate inlets or outlets and used for conveying liquids or... summary from source:
 Manifold Summary
7,578 words, approx. 25 pages
A manifold is an abstract mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be more complicated. In discussing manifolds, the idea of dimension is important. For example,... 
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