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In analogy with the cross-section of a solid, the cross-section of an n-dimensional body in an n-dimensional space is the non-empty intersection of the body with a hyperplane (an (n − 1)-dimensional subspace). This concept has sometimes been used to help visualize aspects of higher dimensional spaces. [7]
For example, when is a vector bundle a section of is an element of the vector space lying over each point . In particular, a vector field on a smooth manifold M {\displaystyle M} is a choice of tangent vector at each point of M {\displaystyle M} : this is a section of the tangent bundle of M {\displaystyle M} .
A section, or cross-section, is a view of a 3-dimensional object from the position of a plane through the object. A section is a common method of depicting the internal arrangement of a 3-dimensional object in two dimensions. It is often used in technical drawing and is traditionally crosshatched. The style of crosshatching often indicates the ...
A local section of a fiber bundle is a continuous map : where U is an open set in B and (()) = for all x in U. If ( U , φ ) {\displaystyle (U,\,\varphi )} is a local trivialization chart then local sections always exist over U .
The two points tracing the cycloids are therefore at equal heights. The line through them is therefore horizontal (i.e. parallel to the two lines on which the circle rolls). Consequently each horizontal cross-section of the circle has the same length as the corresponding horizontal cross-section of the region bounded by the two arcs of cycloids.
The location and shape to cut the outside object depends on many different factors, for example: [1] the sizes and shapes of the inside and outside objects, the semantics of the objects,
A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for example, a solid ball consists of a sphere and its interior. Solid geometry deals with the measurements of volumes of various solids, including pyramids, prisms (and other polyhedrons), cubes, cylinders, cones (and truncated cones). [2]
Cross section (fiber), microscopic view of textile fibers. Section (fiber bundle) , in differential and algebraic geometry and topology, a section of a fiber bundle or sheaf Cross-sectional data , in statistics, econometrics, and medical research, a data set drawn from a single point in time
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