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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]
In geometry, an arrangement of lines is the subdivision of the Euclidean plane formed by a finite set of lines. An arrangement consists of bounded and unbounded convex polygons, the cells of the arrangement, line segments and rays, the edges of the arrangement, and points where two or more lines cross, the vertices of the arrangement.
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} .
In geometry, a curve of constant width is a simple closed curve in the plane whose width (the distance between parallel supporting lines) is the same in all directions. The shape bounded by a curve of constant width is a body of constant width or an orbiform , the name given to these shapes by Leonhard Euler . [ 1 ]
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
In an axiomatic treatment of geometry, the notion of betweenness is either assumed to satisfy a certain number of axioms, or defined in terms of an isometry of a line (used as a coordinate system). Segments play an important role in other theories. For example, in a convex set, the segment that joins any two points of the set is contained in ...
The cross-section of the swept surface in the yz plane now includes a second circle, with equation 0 = ( y + R ) 2 + z 2 − r 2 {\displaystyle 0=(y+R)^{2}+z^{2}-r^{2}\,\!} This pair of circles has two common internal tangent lines , with slope at the origin found from the right triangle with hypotenuse R and opposite side r (which has its ...
The vertical exaggeration is given by: = where VS is the vertical scale and HS is the horizontal scale, both given as representative fractions.. For example, if 1 centimetre (0.39 in) vertically represents 200 metres (660 ft) and 1 centimetre (0.39 in) horizontally represents 4,000 metres (13,000 ft), the vertical exaggeration, 20×, is given by:
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