Paralleel

Paralleel is a term used to describe a relation in which two lines, paths, or flows run in the same direction and do not intersect under defined conditions. In geometry, paralleel lines are contained in a plane and do not meet; they maintain a constant distance apart and have equal direction vectors. The parallel postulate states that through a given point not on a line, there is exactly one line parallel to the given line in a plane. In analytic geometry, two lines with equations of the form ax + by = c and a' x + b' y = c' are parallel if a/a' = b/b' and the lines are distinct.

In three-dimensional space, two lines can be parallel only if they lie in a common plane and do not intersect; lines that do not lie in the same plane and never meet are called skew. Parallelism is a key concept in drawing, architecture, and physics because it implies a consistent direction and spacing.

In computing and data processing, parallelism refers to the execution of multiple computations simultaneously. This includes data parallelism, where the same operation is performed on different data elements, and task parallelism, where different operations are carried out concurrently on possibly different data. Modern hardware such as multi-core processors, graphics processing units (GPUs), and distributed systems enables parallel execution. Software models and frameworks—ranging from threading and vector instructions (SIMD) to distributed computing—address challenges like synchronization, communication overhead, and workload balancing. Parallelism offers potential speedups but is bounded by factors such as algorithm structure and overhead, often described by Amdahl’s law.