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  2. Cross section (geometry) - Wikipedia

    en.wikipedia.org/wiki/Cross_section_(geometry)

    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 ...

  3. Section (fiber bundle) - Wikipedia

    en.wikipedia.org/wiki/Section_(fiber_bundle)

    Sections are studied in homotopy theory and algebraic topology, where one of the main goals is to account for the existence or non-existence of global sections. An obstruction denies the existence of global sections since the space is too "twisted". More precisely, obstructions "obstruct" the possibility of extending a local section to a global ...

  4. Earth section paths - Wikipedia

    en.wikipedia.org/wiki/Earth_section_paths

    The alternative of finding the corresponding point on the section path and computing geodesic distances would produce slightly different results. The first chart is typical of mid-latitude cases where the great ellipse is the outlier. The normal section associated with the point farthest from the equator is a good choice for these cases.

  5. Lemniscate - Wikipedia

    en.wikipedia.org/wiki/Lemniscate

    As he observed, for most such sections the cross section consists of either one or two ovals; however, when the plane is tangent to the inner surface of the torus, the cross-section takes on a figure-eight shape, which Proclus called a horse fetter (a device for holding two feet of a horse together), or "hippopede" in Greek. [8]

  6. Annulus (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Annulus_(mathematics)

    The area of an annulus is the difference in the areas of the larger circle of radius R and the smaller one of radius r: = = = (+) (). As a corollary of the chord formula, the area bounded by the circumcircle and incircle of every unit convex regular polygon is π /4

  7. First moment of area - Wikipedia

    en.wikipedia.org/wiki/First_moment_of_area

    The first moment of area is based on the mathematical construct moments in metric spaces.It is a measure of the spatial distribution of a shape in relation to an axis. The first moment of area of a shape, about a certain axis, equals the sum over all the infinitesimal parts of the shape of the area of that part times its distance from the axis [Σad].

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  9. Section (category theory) - Wikipedia

    en.wikipedia.org/wiki/Section_(category_theory)

    In algebra, sections are also called split monomorphisms and retractions are also called split epimorphisms. In an abelian category , if f : X → Y {\displaystyle f:X\to Y} is a split epimorphism with split monomorphism g : Y → X {\displaystyle g:Y\to X} , then X {\displaystyle X} is isomorphic to the direct sum of Y {\displaystyle Y} and ...

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