par·al·lel / ˈparəˌlel; -ləl/ • adj. (of lines, planes, surfaces, or objects) side by side and having the same distance continuously between them: parallel lines never meet | the road runs parallel to the Ottawa River. ∎ occurring or existing at the same time or in a similar way; corresponding: a parallel universe | they shared an apartment in Dallas while establishing parallel careers. ∎ Comput. involving the simultaneous performance of operations. ∎ of or denoting electrical components or circuits connected to common points at each end, rather than one to another in sequence. The opposite of series. ∎ Mus. containing or denoting successive intervals of the same size in otherwise independent voices: an answering phrase in parallel thirds. ∎ Gram. characterized by parallelism: a parallel structure of transitive clauses.• n. 1. a person or thing that is similar or analogous to another: a challenge that has no parallel in peacetime this century. ∎ a similarity: he points to a parallel between biological evolution and cognitive development. ∎ a comparison: he draws a parallel between personal destiny and social forces.2. (also parallel of latitude) each of the imaginary parallel circles of constant latitude on the earth's surface. ∎ a corresponding line on a map.3. Printing two parallel lines (ǁ) as a reference mark.• v. (-leled, -lel·ing) [tr.] (of something extending in a line) be side by side with (something extending in a line), always keeping the same distance: a big concrete gutter that paralleled the road. ∎ be similar or corresponding to (something): U.S. naval and air superiority was paralleled by Soviet superiority in land-based missile systems.PHRASES: in parallel occurring at the same time and having some connection. ∎ (of electrical components or circuits) connected to common points at each end; not in series.
Generally speaking, parallel means side by side, or the concept where any two or more things neither converge nor diverge from one another.
In geometry, a part of mathematics, parallel means that two or more lines or planes (within Euclidean space) do not intersect (cross) one another. Lines are parallel in Euclidean two-dimensional space if they reside within the same plane and do not intersect. Likewise, planes are parallel in Euclidean three-dimensional space if they do not intersect each other. These planes must keep a constant distance between points closest to each other on the two lines. Lines in three-dimensional space are called skew lines if they are not parallel to one another.
Thus, two or more lines (or planes) are said to be parallel if they lie in the same plane (or space) and have no point in common, no matter how far they are extended.
Mathematical notation for parallel isǀ. For example, for two lines that are parallel to one another, such as line A is parallel to line B, the notation would look like: AǀB.
Greek mathematician Euclid of Alexandria (c. 325–265 BC) formulated his fifth postulate, which revolves around the concept of parallel lines. It basically states that given any straight line A and any point c not on that line, then one and only one other straight line B exists that passes through point c but does not pass through the first line A, no matter how far both lines A and B are extended in either direction.
So parallelepiped XVII (in Gr. form XVI). — Gr. parallēlepípedon, f. parállēlos + epipedon plane surface, sb. use of n. of epípedos plane, f. EPI- + pédon ground. parallelogram XVI. — F. parallélogramme — late L. parallēlogrammum — Gr. parallelógrammon, sb. use of n. of adj. f. parállēlos + grammḗ line (cf. -GRAM).