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The second is a ''shape effect'' that results from the artificial shape delineated by the boundary. As an illustration of the effect of the artificial shape, point pattern analysis tends to provide higher levels of clustering for the identical point pattern within a unit that is more elongated.<ref name=Fotheringham93/> Similarly, the shape can influence interaction and flow among spatial entities.<ref>{{cite journal |last1=Arlinghaus |first1=Sandra L. |last2=Nystuen |first2=John D. |title=Geometry of Boundary Exchanges |journal=Geographical Review |date=January 1990 |volume=80 |issue=1 |pages=21 |doi=10.2307/215895|jstor=215895 }}</ref><ref>{{cite journal |last1=Ferguson |first1=Mark R. |last2=Kanaroglou |first2=Pavlos S. |title=Representing the Shape and Orientation of Destinations in Spatial Choice Models |journal=Geographical Analysis |date=3 September 2010 |volume=30 |issue=2 |pages=119–137 |doi=10.1111/j.1538-4632.1998.tb00392.x|doi-access=free }}</ref><ref>{{cite journal |last1=Griffith |first1=Daniel A. |title=Geometry and Spatial Interaction |journal=Annals of the Association of American Geographers |date=1982 |volume=72 |issue=3 |pages=332–346 |issn=0004-5608|jstor=2563023 |doi=10.1111/j.1467-8306.1982.tb01829.x }}</ref> For example, the shape can affect the measurement of origin-destination flows since these are often recorded when they cross an artificial boundary. Because of the effect set by the boundary, the shape and area information is used to estimate travel distances from surveys,<ref>{{cite journal |last1=Rogerson |first1=Peter A. |title=Buffon's needle and the estimation of migration distances |journal=Mathematical Population Studies |date=July 1990 |volume=2 |issue=3 |pages=229–238 |doi=10.1080/08898489009525308|pmid=12283029 }}</ref> or to locate traffic counters, travel survey stations, or traffic monitoring systems.<ref>Kirby, H. R. (1997) Buffon's needle and the probability of intercepting short-distance trips by multiple screen-line surveys. Geographical Analysis, 29 64–71.</ref> From the same perspective, Theobald (2001; retrieved from<ref name=BESR02/>) argued that measures of urban sprawl should consider interdependences and interactions with nearby rural areas.
In spatial analysis, the boundary problem has been discussed along with the [[modifiable areal unit problem]] (MAUP) inasmuch as MAUP is associated with the arbitrary geographic unit and the unit is defined by the boundary.<ref>{{cite book |last1=Rogerson |first1=Peter A. |title=Statistical methods for geography : a student guide |date=2006 |publisher=SAGE |isbn=978-1412907965 |edition=2nd}}</ref> For administrative purposes, data for policy indicators are usually aggregated within larger units (or enumeration units) such as census tracts, school districts, municipalities and counties.<ref name=Openshaw1>{{cite book |last1=Openshaw |first1=Stan |title=The Modifiable Areal Unit Problem |date=1983 |isbn=0 86094 134 5 |url=https://alexsingleton.files.wordpress.com/2014/09/38-maup-openshaw.pdf}}</ref><ref name=Chen1>{{cite journal |last1=Chen |first1=Xiang |last2=Ye |first2=Xinyue |last3=Widener |first3=Michael J. |last4=Delmelle |first4=Eric |last5=Kwan |first5=Mei-Po |last6=Shannon |first6=Jerry |last7=Racine |first7=Racine F. |last8=Adams |first8=Aaron |last9=Liang |first9=Lu |last10=Peng |first10=Jia |title=A systematic review of the modifiable areal unit problem (MAUP) in community food environmental research |journal=Urban Informatics |date=27 December 2022 |volume=1 |doi=10.1007/s44212-022-00021-1 |url=https://link.springer.com/article/10.1007/s44212-022-00021-1 |access-date=27 December 2022}}</ref> The artificial units serve the purposes of taxation and service provision. For example, municipalities can effectively respond to the need of the public in their jurisdictions. However, in such spatially aggregated units, spatial variations of detailed social variables cannot be identified. The problem is noted when the average degree of a variable and its unequal distribution over space are measured.<ref name=BESR02/>
== Suggested solutions and evaluations on the solutions ==
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