parallelliset

Parallelliset is the Finnish term commonly used in geometry to describe two or more elements that do not intersect and remain at a constant distance from each other. The concept applies to lines, planes, and other geometric objects that share the same direction.

In a two-dimensional Euclidean plane, two distinct lines are parallel if they never meet. They have the same slope, or they are both vertical (in which case their x-coordinates are constant and they do not intersect). The distance between parallel lines is constant at every point.

When a transversal intersects parallel lines, corresponding angles are equal and alternate interior angles are equal as well. The constancy of separation implies many predictable geometric relationships, useful in design, architecture, and surveying.

In three-dimensional space, the idea extends to parallel planes: two planes are parallel if their normal vectors are parallel, in which case every line perpendicular to the planes maintains the same distance to both.

In non-Euclidean geometries, the notion of parallelism can differ. For example, on the surface of a sphere, great circles that start parallel will eventually converge, so traditional Euclidean parallelism does not hold. In hyperbolic geometry, there can be infinitely many lines through a point that do not intersect a given line.

Parallelliset are foundational in mathematics and practical activities such as drafting, computer graphics, and civil engineering, where consistent direction and spacing are essential. The term is standard in Finnish mathematical literature and education.