tasapinda

Tasapinda is the partitive singular form of the Estonian noun tasapind, meaning plane in geometry. In mathematics, tasapind refers to a flat, two-dimensional surface that extends without bound in every direction, embedded in three-dimensional space. A plane can be defined algebraically by the equation ax + by + cz + d = 0, where (a, b, c) is a nonzero normal vector. Equivalently, a plane can be described as the set of points r = P0 + s u + t v, where P0 is a point on the plane and u, v are two non-collinear direction vectors lying in the plane.

Two planes in three-dimensional space either intersect in a line, are parallel, or are coincident. The distance from a point X to a plane ax + by + cz + d = 0 is |a x0 + b y0 + c z0 + d| / sqrt(a^2 + b^2 + c^2). Planes form the backbone of analytic geometry and are used to model surfaces, perform intersections, shading in computer graphics, and many engineering calculations. Planes are affine subspaces of dimension 2; any three non-collinear points determine a unique plane.

In Estonian grammar, tasapinda is the partitive singular form of tasapind, used where the language requires the partitive case. The term is thus relevant both as a geometric concept and as a grammatical inflection in Estonian.