the mathematical aspect of cartographic mapping is a process which establishes a unique connection between points of the earth’s sphere and their images on a plane. it was proven in differential geometry that an isometric mapping of a sphere onto a plane with all corresponding distances on both surfaces remaining identical can never be achieved since the two surfaces do not possess the same gau...

After decades of using only one map projection, the Polyconic, for its mapping program, the U.S. Geological Survey (USGS) now uses several of the more common projections for its published maps. For larger scale maps, including topographic quadrangles and the State Base Map Series, conformal projections such as the Transverse Mercator and the Lambert Conformal Conic are used. Equal-area and equi...

the mathematical aspect of cartographic mapping is a process which establishes a unique connection between points of the earth’s sphere and their images on a plane. it was proven in differential geometry that an isometric mapping of a sphere onto a plane with all corresponding distances on both surfaces remaining identical can never be achieved since the two surfaces do not possess the same gau...

We consider a family of conformal (angle preserving) projections of the sphere onto the plane. The family is referred to as the Lambert conic conformal projections. Special cases include the Mercator map and the stereographic projection. The techniques only involve elementary calculus and trigonometry.

Conic map projections are appropriate for mapping regions at medium and large scales with east–west extents at intermediate latitudes. Conic projections are appropriate for these cases because they show the mapped area with less distortion than other projections. In order to minimize the distortion of the mapped area, the two standard parallels of conic projections need to be selected carefully...

It is useful to have mathematical criteria for evaluating errors in map projections. The Chebyshev criterion for minimizing rms (root mean square) local scale factor errors for conformal maps has been useful in developing conformal map projections of continents. However, any local error criterion will be minimized ultimately by map projections with multiple interruptions. A disadvantage of inte...