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Euclid's Elements defines a straight line as a "breadthless length" that "lies evenly with respect to the points on itself", and introduced several postulates as basic unprovable properties on which the rest of geometry was established. Euclidean line and Euclidean geometry are terms introduced to avoid confusion with generalizations introduced ...
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 .
In inversive geometry, a line is a degenerate case of a circle, with infinite radius. Two parallel lines also form a degenerate parabola. A line segment can be viewed as a degenerate case of an ellipse in which the semiminor axis goes to zero, the foci go to the endpoints, and the eccentricity goes to one.
Common geometric terms of location are: Radial (solid and colored lines) and circumferential roads (dashed and gray lines) in Metro Manila's road network. Axial – along the center of a round body, or the axis of rotation of a body; Radial – along a direction pointing along a radius from the center of an object, or perpendicular to a curved ...
In any affine space (including a Euclidean space) the set of lines parallel to a given line (sharing the same direction) is also called a pencil, and the vertex of each pencil of parallel lines is a distinct point at infinity; including these points results in a projective space in which every pair of lines has an intersection.
Line a is a great circle, the equivalent of a straight line in spherical geometry. Line c is equidistant to line a but is not a great circle. It is a parallel of latitude. Line b is another geodesic which intersects a in two antipodal points. They share two common perpendiculars (one shown in blue).
Thus, a line segment AB defined as the points A and B and all the points between A and B in absolute geometry, needs to be reformulated. A line segment in this new geometry is determined by three collinear points A, B and C and consists of those three points and all the points not separated from B by A and C. There are further consequences.
Common lines and line segments on a circle, including a secant. A straight line can intersect a circle at zero, one, or two points. A line with intersections at two points is called a secant line, at one point a tangent line and at no points an exterior line. A chord is the line segment that joins two distinct points of a circle. A chord is ...
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