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A plane containing a cross-section of the solid may be referred to as a cutting plane. The shape of the cross-section of a solid may depend upon the orientation of the cutting plane to the solid. For instance, while all the cross-sections of a ball are disks, [2] the cross-sections of a cube depend on how the cutting plane is related to the ...
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.
In the mathematical field of topology, a section (or cross section) [1] of a fiber bundle is a continuous right inverse of the projection function. In other words, if E {\displaystyle E} is a fiber bundle over a base space , B {\displaystyle B} :
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations.This means that, compared to elementary Euclidean geometry, projective geometry has a different setting (projective space) and a selective set of basic geometric concepts.
Thus, the cross-section of a circular cylinder perpendicular to the axis of the cylinder is a disk, not a circle (which is the boundary of that disk). Some of this confusion is probably due to the long standing abuse of notation found in elementary geometry where, for example, a circle could mean either a disk or the boundary of that disk ...
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A necessary and sufficient condition for (, /,,) to form a fiber bundle is that the mapping admits local cross-sections (Steenrod 1951, §7). The most general conditions under which the quotient map will admit local cross-sections are not known, although if G {\displaystyle G} is a Lie group and H {\displaystyle H} a closed subgroup (and thus a ...
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