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  2. Line segment - Wikipedia

    en.wikipedia.org/wiki/Line_segment

    A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry , a line segment is often denoted using an overline ( vinculum ) above the symbols for the two endpoints, such as in AB .

  3. Manifold - Wikipedia

    en.wikipedia.org/wiki/Manifold

    Manifolds need not be closed; thus a line segment without its end points is a manifold. They are never countable, unless the dimension of the manifold is 0. Putting these freedoms together, other examples of manifolds are a parabola, a hyperbola, and the locus of points on a cubic curve y 2 = x 3 − x (a closed loop piece and an open, infinite ...

  4. Constructible number - Wikipedia

    en.wikipedia.org/wiki/Constructible_number

    The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.

  5. Line integral - Wikipedia

    en.wikipedia.org/wiki/Line_integral

    When L is a closed curve (initial and final points coincide), the line integral is often denoted (), sometimes referred to in engineering as a cyclic integral. To establish a complete analogy with the line integral of a vector field, one must go back to the definition of differentiability in multivariable calculus.

  6. Convex set - Wikipedia

    en.wikipedia.org/wiki/Convex_set

    Equivalently, a convex set or a convex region is a set that intersects every line in a line segment, single point, or the empty set. [1] [2] For example, a solid cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex. The boundary of a convex set in the plane is always a convex curve.

  7. Generalized Stokes theorem - Wikipedia

    en.wikipedia.org/wiki/Generalized_Stokes_theorem

    In particular, the fundamental theorem of calculus is the special case where the manifold is a line segment, Green’s theorem and Stokes' theorem are the cases of a surface in or , and the divergence theorem is the case of a volume in . [2] Hence, the theorem is sometimes referred to as the fundamental theorem of multivariate calculus.

  8. Intersection (geometry) - Wikipedia

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

    In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the lineline intersection between two distinct lines, which either is one point (sometimes called a vertex) or does not exist (if the lines are parallel). Other types ...

  9. Contour integration - Wikipedia

    en.wikipedia.org/wiki/Contour_integration

    Then, we use the so-called keyhole contour, which consists of a small circle about the origin of radius ε say, extending to a line segment parallel and close to the positive real axis but not touching it, to an almost full circle, returning to a line segment parallel, close, and below the positive real axis in the negative sense, returning to ...