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South-up map orientation is the orientation of a map with south up, at the top of the map, amounting to a 180-degree rotation of the map from the standard convention of north-up. Maps in this orientation are sometimes called upside down maps or reversed maps. [citation needed] Other maps with non-standard orientation include T and O maps, polar ...
Cardinal directions or cardinal points may sometimes be extended to include vertical position (elevation, altitude, depth): north and south, east and west, up and down; or mathematically the six directions of the x-, y-, and z-axes in three-dimensional Cartesian coordinates. Topographic maps include elevation, typically via contour lines.
A map is a function, as in the association of any of the four colored shapes in X to its color in Y. In mathematics, a map or mapping is a function in its general sense. [1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper. [2]
A torus is an orientable surface The Möbius strip is a non-orientable surface. Note how the disk flips with every loop. The Roman surface is non-orientable.. In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "anticlockwise". [1]
The Fra Mauro world map is unusual, but typical of Fra Mauro's portolan charts, in that its orientation is with the south at the top. One explanation for why the map places south at the top is that 15th-century compasses were south-pointing. [6] In addition, south at the top was used in Arab maps of the time.
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The circle inversion map is anticonformal, which means that at every point it preserves angles and reverses orientation (a map is called conformal if it preserves oriented angles). Algebraically, a map is anticonformal if at every point the Jacobian is a scalar times an orthogonal matrix with negative determinant: in two dimensions the Jacobian ...
Sergeant Chris D. Washington checking his Topographic map during a morning deer hunt in Kilgore, Texas A topographic map of Stowe, Vermont with contour lines Part of the same map in a perspective shaded relief view illustrating how the contour lines follow the terrain Sheet #535 (2013 version; second digital edition) of MTN50 Spanish National Topographic map series, covering Algete town (near ...