puolitasoja

A puolitasoja is a Finnish term that translates to "half-plane" in English. In mathematics, a half-plane is a region of a plane that is divided by a straight line. The line itself is called the boundary of the half-plane. A half-plane can be open or closed, depending on whether the boundary line is included in the region.

An open half-plane does not include its boundary line, while a closed half-plane includes the boundary line. Mathematically, a half-plane can be represented by an inequality. For example, in a two-dimensional Cartesian coordinate system, the line might be represented by the equation Ax + By = C. An open half-plane could then be represented by Ax + By < C or Ax + By > C. A closed half-plane would be represented by Ax + By <= C or Ax + By >= C.

Half-planes are fundamental concepts in geometry and have applications in various fields. They are used in defining convex sets, in linear programming to represent constraints, and in computational geometry. The concept can be extended to higher dimensions, where a hyperplane divides a space into two half-spaces.