Direction (geometry)

Direction is the information contained in the relative position of one point with respect to another point without the distance information. Directions may be either relative to some indicated reference (the violins in a full orchestra are typically seated to the left of the conductor), or absolute according to some previously agreed upon frame of reference (New York City lies due west of Madrid). Direction is often indicated manually by an extended index finger or written as an arrow. On a vertically oriented sign representing a horizontal plane, such as a road sign, "forward" is usually indicated by an upward arrow. Mathematically, direction may be uniquely specified by a unit vector, or equivalently by the angles made by the most direct path with respect to a specified set of axes.

See also

Geography

Geography (from Greek γεωγραφία, geographia, lit. "earth description") is a field of science devoted to the study of the lands, the features, the inhabitants, and the phenomena of Earth. A literal translation would be "to describe or picture or write about the earth". The first person to use the word "geography" was Eratosthenes (276–194 BC). Four historical traditions in geographical research are spatial analysis of the natural and the human phenomena (geography as the study of distribution), area studies (places and regions), study of the human-land relationship, and research in the Earth sciences. Nonetheless, modern geography is an all-encompassing discipline that foremost seeks to understand the Earth and all of its human and natural complexities—not merely where objects are, but how they have changed and come to be. Geography has been called "the world discipline" and "the bridge between the human and the physical science". Geography is divided into two main branches: human geography and physical geography.

Geometry

Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of formal mathematical science emerging in the West as early as Thales (6th century BC). By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially as it relates to mapping the positions of stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. In the classical world, both geometry and astronomy were considered to be part of the Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.

Direction

Direction may refer to:

Cardinal direction

The four cardinal directions or cardinal points are the directions of north, east, south, and west, commonly denoted by their initials: N, E, S, W. East and west are at right angles to north and south, with east being in the clockwise direction of rotation from north and west being directly opposite east. Intermediate points between the four cardinal directions form the points of the compass. The intermediate (intercardinal, or ordinal) directions are northeast (NE), southeast (SE), southwest (SW), and northwest (NW). Further, the intermediate direction of every set of intercardinal and cardinal direction is called a secondary-intercardinal direction, the eight shortest points in the compass rose to the right, i.e. NNE, ENE, ESE, and so on.

Locating the directions

Direction versus bearing

To keep to a bearing is not, in general, the same as going in a straight direction along a great circle. Conversely, one can keep to a great circle and the bearing may change. Thus the bearing of a straight path crossing the North Pole changes abruptly at the Pole from North to South. When travelling East or West, it is only on the Equator that one can keep East or West and be going straight (without need to steer). Anywhere else, maintaining latitude requires a change in direction, requires steering. However, this change in direction becomes increasingly negligible as one moves to lower latitudes.