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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} .
Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.
In geometry, an envelope of a planar family of curves is a curve that is tangent to each member of the family at some point, and these points of tangency together form the whole envelope. Classically, a point on the envelope can be thought of as the intersection of two " infinitesimally adjacent" curves, meaning the limit of intersections of ...
The Reuleaux triangle has been used as the shape for the cross section of a fire hydrant valve nut. The constant width of this shape makes it difficult to open the fire hydrant using standard parallel-jawed wrenches; instead, a wrench with a special shape is needed.
Template: General geometry. 22 languages. ... Print/export Download as PDF; Printable version; In other projects Wikidata item;
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related to: geometry cross section examples pdf notes printable template for therapy sessions