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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 .
[1] [2] A diagram showing a representative set of neighboring field lines is a common way of depicting a vector field in scientific and mathematical literature; this is called a field line diagram. They are used to show electric fields , magnetic fields , and gravitational fields among many other types.
Closed line or closed lines could refer to: Closed curve, a curve in mathematics where the two ends meet; Closed line segment, a line segment in mathematics that includes both its endpoints; Defunct airlines, or air travel companies that no longer exist; Line (formation), a military formation in which soldiers are packed together into rows
The normal form (also called the Hesse normal form, [10] after the German mathematician Ludwig Otto Hesse), is based on the normal segment for a given line, which is defined to be the line segment drawn from the origin perpendicular to the line. This segment joins the origin with the closest point on the line to the origin.
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 ...
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.
A convex set in light blue, and its extreme points in red. Throughout, will be a real or complex vector space. For any elements and in a vector space, the set [,]:= {+ ():} is called the closed line segment or closed interval between and .
A set C is strictly convex if every point on the line segment connecting x and y other than the endpoints is inside the topological interior of C. A closed convex subset is strictly convex if and only if every one of its boundary points is an extreme point. [3] A set C is absolutely convex if it is convex and balanced.