Planaritás

Planaritás is a fundamental concept in geometry referring to the property of lying within a single plane. A set of points is planar if all of them can be contained within the same two-dimensional surface. For example, the vertices of a triangle are always planar, as are the points forming a square or a circle.

In three-dimensional space, a plane is a flat, two-dimensional surface that extends infinitely. If all the points of a given geometric object or collection of points can be found on such a plane, the object or collection is said to be planar. Conversely, if even one point lies outside this plane, the set is non-planar.

The concept of planarity is crucial in various fields. In computer graphics, determining if a set of 3D points forms a planar surface is essential for rendering and modeling. In surveying and cartography, understanding the planarity of terrain features is important for creating accurate maps. In mathematics, theorems and proofs often rely on the assumption or demonstration of planarity for specific geometric configurations. For instance, a fundamental property is that any three non-collinear points define a unique plane, thus making them always planar.