tasapind

Tasapind is the Estonian term for the geometric concept known in English as a plane. It refers to a flat, two-dimensional subset of three-dimensional space that extends without bound in all directions and has no thickness. In Euclidean geometry, a tasapind is characterized by being flat and by containing infinitely many lines and points.

A plane can be described in several equivalent ways. In three-dimensional space, it can be defined by a linear equation of the form ax + by + cz + d = 0, where a, b, and c are not all zero and the vector n = (a, b, c) is normal (perpendicular) to the plane. An alternative description is that the plane consists of all points p for which the dot product with the normal vector satisfies n · p = d. The plane is fully determined by three non-collinear points, or by a line together with a point not on that line, or by the intersection of two non-parallel planes.

Within a tasapind, any two points determine a unique line, and any two lines lie either in the same plane and intersect, or are parallel. Common examples include the coordinate planes, such as the xy-plane defined by z = 0, the yz-plane defined by x = 0, and the xz-plane defined by y = 0.

Planes have wide-ranging applications in mathematics, computer graphics, CAD, and GIS. They are used to model surfaces, define tangents to curves, and determine intersections, such as the line of intersection between two planes.