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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 .
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.
A chord (from the Latin chorda, meaning "bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a secant line. The perpendicular line passing through the chord's midpoint is called sagitta (Latin for "arrow").
In some situations phrasing results in terms of secant lines instead of chords can help to unify statements. As an example of this consider the result: [5] If two secant lines contain chords AB and CD in a circle and intersect at a point P that is not on the circle, then the line segment lengths satisfy AP⋅PB = CP⋅PD.
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. [1] In a polygon, an edge is a line segment on the boundary, [2] and is often called a polygon side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces (or polyhedron sides ...
The Encyclopedia of Mathematics [7] defines interval (without a qualifier) to exclude both endpoints (i.e., open interval) and segment to include both endpoints (i.e., closed interval), while Rudin's Principles of Mathematical Analysis [8] calls sets of the form [a, b] intervals and sets of the form (a, b) segments throughout.
However, in the generalization to affine geometry, where segment lengths are not defined, [5] the midpoint can still be defined since it is an affine invariant. The synthetic affine definition of the midpoint M of a segment AB is the projective harmonic conjugate of the point at infinity, P, of the line AB. That is, the point M such that H[A,B ...
The line determined by the points of intersection of the two circles is the perpendicular bisector of the segment. Because the construction of the bisector is done without the knowledge of the segment's midpoint , the construction is used for determining as the intersection of the bisector and the line segment.