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In physics and mathematics, two-dimensional space or bi-dimensional space is a geometric model of the planar projection of the physical universe. The two dimensions are commonly called length and width. Both directions lie in the same plane. A sequence of ''n'' real numbers can be understood as a location in ''n''-dimensional space. When ''n'' = 2, the set of all such locations is called two-dimensional space or bi-dimensional space, and usually is thought of as a Euclidean space. ==History== Books I through IV and VI of Euclid's Elements dealt with two-dimensional geometry, developing such notions as similarity of shapes, the Pythagorean theorem (Proposition 47), equality of angles and areas, parallelism, the sum of the angles in a triangle, and the three cases in which triangles are "equal" (have the same area), among many other topics. Later, the plane was described in a so-called ''Cartesian coordinate system'', a coordinate system that specifies each point uniquely in a plane by a pair of numerical ''coordinates'', which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a ''coordinate axis'' or just ''axis'' of the system, and the point where they meet is its ''origin'', usually at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin. The idea of this system was developed in 1637 in writings by Descartes and independently by Pierre de Fermat, although Fermat also worked in three dimensions, and did not publish the discovery. Both authors used a single axis in their treatments and have a variable length measured in reference to this axis. The concept of using a pair of axes was introduced later, after Descartes' ''La Géométrie'' was translated into Latin in 1649 by Frans van Schooten and his students. These commentators introduced several concepts while trying to clarify the ideas contained in Descartes' work. Later, the plane was thought of as a field, where any two points could be multiplied and, except for 0, divided. This was known as the complex plane. The complex plane is sometimes called the Argand plane because it is used in Argand diagrams. These are named after Jean-Robert Argand (1768–1822), although they were first described by Norwegian-Danish land surveyor and mathematician Caspar Wessel (1745–1818).〔Wessel's memoir was presented to the Danish Academy in 1797; Argand's paper was published in 1806. (Whittaker & Watson, 1927, p. 9)〕 Argand diagrams are frequently used to plot the positions of the poles and zeroes of a function in the complex plane. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Two-dimensional space」の詳細全文を読む スポンサード リンク
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