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A boundary problem in analysis is a phenomenon in which geographical patterns are differentiated by the shape and arrangement of boundaries that are drawn for administrative or measurement purposes. The boundary problem occurs because of the loss of neighbors in analyses that depend on the values of the neighbors.
For example, census data may be aggregated into county districts, census tracts, postcode areas, police precincts, or any other arbitrary spatial partition. Thus the results of data aggregation are dependent on the mapmaker's choice of which "modifiable areal unit" to use in their analysis.
One such example is the Rio Grande, which defines part of the border between the United States and Mexico, whose movement has led to multiple conflicts. Natural borders are not to be confused with landscape borders, which are also geographical features that demarcate political boundaries.
A megalopolis, following the work of Gottmann, refers to two or more roughly adjacent metropolitan areas that, through a commonality of systems—e.g., of transport, economy, resources, and ecologies—experience a blurring of the boundaries between the population centers, [2] such that while some degree of separation may remain, their ...
1953 — Following the Korean War, the boundary between North Korea and South Korea is the Military Demarcation Line, which roughly follows the previous 38th parallel; 1954 — Bands of Indian irregulars took over the Portuguese enclaves of Dadra and Nagar Haveli. On June 13, the port of Mahé breaks away from French rule and joins India.
A manifold with boundary is a manifold with an edge. For example, a sheet of paper is a 2-manifold with a 1-dimensional boundary. The boundary of an -manifold with boundary is an ()-manifold. A disk (circle plus interior) is a 2-manifold with boundary. Its boundary is a circle, a 1-manifold.
This was the beginning of the coastline problem, which is a mathematical uncertainty inherent in the measurement of boundaries that are irregular. [6] The prevailing method of estimating the length of a border (or coastline) was to lay out n equal straight-line segments of length l with dividers on a map or aerial photograph. Each end of the ...
Polish-East German Maritime Boundary in Pomeranian Bay Delimitation Treaty (1989) German-Polish Border Treaty (1990) Two Plus Four Treaty (1991) Treaty of Good Neighbourship (1991) Poland–Slovakia Border Adjustment (2005) Polish-Danish Maritime Boundary Delimitation Agreement (2018)