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  2. Cross section (geometry) - Wikipedia

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

    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 cube. If the cutting plane is perpendicular to a line joining the centers of two opposite faces of the cube, the cross-section will be a square, however, if the cutting plane is perpendicular to a ...

  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. Fiber bundle - Wikipedia

    en.wikipedia.org/wiki/Fiber_bundle

    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 ...

  5. UBASIC - Wikipedia

    en.wikipedia.org/wiki/UBASIC

    The help files have articles and lessons for beginners. UBASIC has a built-in on-line editor with several aids for debugging. It can show cross references to calling lines, lines containing a variable, and lists of variables/arrays. It can renumber lines, change variable names, and append additional programs.

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  7. 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]

  8. Projective geometry - Wikipedia

    en.wikipedia.org/wiki/Projective_geometry

    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.

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