Search results
Results from the WOW.Com Content Network
The maturation of complex analysis led to general techniques for conformal mapping, where points of a flat surface are handled as numbers on the complex plane.While working at the United States Coast and Geodetic Survey, the American philosopher Charles Sanders Peirce published his projection in 1879, [2] having been inspired by H. A. Schwarz's 1869 conformal transformation of a circle onto a ...
The polytopes of rank 2 (2-polytopes) are called polygons.Regular polygons are equilateral and cyclic.A p-gonal regular polygon is represented by Schläfli symbol {p}.. Many sources only consider convex polygons, but star polygons, like the pentagram, when considered, can also be regular.
The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.
Lines of constant bearing (rhumb lines) are straight, aiding navigation. Areas inflate with latitude, becoming so extreme that the map cannot show the poles. 2005 Web Mercator: Cylindrical Compromise Google: Variant of Mercator that ignores Earth's ellipticity for fast calculation, and clips latitudes to ~85.05° for square presentation. De ...
The various cylindrical projections are distinguished from each other solely by their north-south stretching (where latitude is given by φ): The only normal cylindrical projections that preserve area have a north-south compression precisely the reciprocal of east-west stretching (cos φ). This divides north-south distances by a factor equal to ...
North-south stretching grows with latitude, but less quickly than the east-west stretching: such as the Miller cylindrical projection (sec 4 / 5 φ). North-south distances neither stretched nor compressed (1): equirectangular projection or "plate carrée". North-south compression equals the cosine of the latitude (the reciprocal of east ...
With no distortion along the central meridian and the equator, distances along those lines are correct, as are the angles of intersection of other lines with those two lines. Distortion is lowest throughout the region of the map close to those lines. A sinusoidal projection shows relative sizes accurately, but distorts shapes and directions.
Grid lines of the transverse projection, other than the x and y axes, do not run north-south or east-west as defined by parallels and meridians. This is evident from the global projections shown above. Near the central meridian the differences are small but measurable. The difference between the north-south grid lines and the true meridians is ...