Intersections

Intersections are the points or regions where two or more objects meet or share common elements. The idea appears in many branches of science and daily life, from abstract mathematics to road design.

In set theory, the intersection of sets A and B, denoted A ∩ B, consists of all elements that belong to both A and B. The operation extends to any collection of sets and is both commutative and associative. Intersections are complemented by unions; De Morgan's laws relate the two operations.

In geometry, an intersection is where geometric figures meet. The intersection of two lines is a point unless the lines are parallel, in which case there is no intersection; if the lines coincide, their intersection is the line itself. The intersection of two planes is a line. Intersections with curves or surfaces can yield points, lines, or more complex sets, depending on the shapes involved.

In computation and computational geometry, intersection problems ask whether two geometric objects intersect and, when they do, to determine the intersection set. Efficient algorithms exist for line segments, polygons, and higher-order curves, with applications in computer graphics, geographic information systems, and collision detection.

In urban design, a road intersection is a junction where two or more streets cross or meet, typically managed by traffic controls such as signs, signals, or roundabouts to regulate flow and safety.