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Differential geometry can either be intrinsic (meaning that the spaces it considers are smooth manifolds whose geometric structure is governed by a Riemannian metric, which determines how distances are measured near each point) or extrinsic (where the object under study is a part of some ambient flat Euclidean space).
Normally, entries of a glossary are structured by topics and sorted alphabetically. This is not possible here, as there is no natural order on symbols, and many symbols are used in different parts of mathematics with different meanings, often completely unrelated. Therefore, some arbitrary choices had to be made, which are summarized below.
Smoothness is a concept which mathematics has endowed with many meanings, from simple differentiability to infinite differentiability to analyticity, and still others which are more complicated. Each such usage attempts to invoke the physically intuitive notion of smoothness. strong, stronger
This is a glossary of algebraic geometry. See also glossary of commutative algebra , glossary of classical algebraic geometry , and glossary of ring theory . For the number-theoretic applications, see glossary of arithmetic and Diophantine geometry .
Solid geometry, including table of major three-dimensional shapes; Box-drawing character; Cuisenaire rods (learning aid) Geometric shape; Geometric Shapes (Unicode block) Glossary of shapes with metaphorical names; List of symbols; Pattern Blocks (learning aid)
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
The following definitions are also fundamental to algebraic topology, differential topology and geometric topology. For a list of terms specific to algebraic topology, see Glossary of algebraic topology. All spaces in this glossary are assumed to be topological spaces unless stated otherwise.
In mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.
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related to: basic geometry terms definitions and meanings