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...

Abstract Maps that correctly represent the geographic size and shape of regions, taking into account scaling generalization, have disadvantage small regions can easily be overlooked or not seen at all. Hence, for some map use tasks where are importance, alternative types needed. One option is so-called equal area unit maps (EAUMs), every enumeration has same size, possibly also basic such as sq...

In this paper, we consider the problem of packing two or more equal area polygons with disjoint interiors into a convex body K in E such that each of them has at most a given number of sides. We show that for a convex quadrilateral K of area 1, there exist n internally disjoint triangles of equal area such that the sum of their areas is at least 4n 4n+1 . We also prove results for other types o...