DIMENSION

in geometry, a magnitude measured in a specific direction, as, for example, along a diameter or a principal axis or an edge. A point is said to be without dimension; a line has the one dimension of length, a surface has the two dimensions of length and breadth, while a solid has the three dimensions of length, breadth, and thickness. Since the lengths of lines, the areas of surfaces, and the volumes of solids are represented respectively by linear, quadratic, and cubic algebraic expressions, the term dimension has been carried over into algebra. Thus quadratic, cubic, and biquadratic algebraic expressions (e.g., x2, x3, x4) or equations are said to be respectively of two, three, and four dimensions (or degree or order). Similarly, the term dimension is used in mechanics with reference to the units of time, length, and mass and various derived units, and it occurs in many other parts of physics, notably in the theory of electricity and magnetism.