Coplanares

Coplanares is a term used in geometry to describe points that lie on the same plane. A plane is a two-dimensional flat surface that extends infinitely in all directions. If a set of points can all be found within a single, flat surface, then those points are considered coplanar. The concept of coplanarity is fundamental in understanding spatial relationships between objects and lines in three-dimensional space.

For example, any three non-collinear points are always coplanar, as they define a unique plane. However, four or more points may or may not be coplanar. If four points lie on the same plane, they are coplanar. If even one of those points is not on that plane, then all four points are not coplanar. This principle is important in fields like surveying, engineering, and computer graphics where precise spatial arrangements are critical. Determining coplanarity often involves checking if a set of points satisfies the equation of a plane, or by demonstrating that a plane can be constructed that contains all the given points.