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The Pennsylvania Railroad's class K5 were experimental 4-6-2 "Pacific" types, built in 1929 to see if a larger Pacific than the standard K4s was worthwhile. Two prototypes were built, #5698 at the PRR's own Altoona Works, and #5699 by the Baldwin Locomotive Works. Although classified identically, the two locomotives differed in many aspects, as ...
Analogous to straight line segments above, one can also define arcs as segments of a curve. In one-dimensional space, a ball is a line segment. An oriented plane segment or bivector generalizes the directed line segment. Beyond Euclidean geometry, geodesic segments play the role of line segments.
Intersection of two line segments. For two non-parallel line segments (,), (,) and (,), (,) there is not necessarily an intersection point (see diagram), because the intersection point (,) of the corresponding lines need not to be contained in the line segments. In order to check the situation one uses parametric representations of the lines:
The word line may also refer, in everyday life, to a line segment, which is a part of a line delimited by two points (its endpoints). 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 ...
The Shamos–Hoey algorithm [1] applies this principle to solve the line segment intersection detection problem, as stated above, of determining whether or not a set of line segments has an intersection; the Bentley–Ottmann algorithm works by the same principle to list all intersections in logarithmic time per intersection.
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 ...
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.
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).