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A common use of distance cartograms is to show the relative travel times and directions from vertices in a network. For example, on a distance cartogram showing travel time between cities, the less time required to get from one city to another, the shorter the distance on the cartogram will be.
Proximity analysis is a class of spatial analysis tools and algorithms that employ geographic distance as a central principle. [1] Distance is fundamental to geographic inquiry and spatial analysis, due to principles such as the friction of distance, Tobler's first law of geography, and Spatial autocorrelation, which are incorporated into analytical tools. [2]
The gravity model of migration is a model in urban geography derived from Newton's law of gravity, and used to predict the degree of migration interaction between two places. [1] In 1941, astrophysicist John Q. Stewart [ 2 ] applied Newton's law to the social sciences, establishing a theoretical foundation for the field of social physics.
Spatial diffusion is the gradual spread of culture, ideas, and institutions across space over time, in which the desirability of one place adopting the traits of a separate place overcome the friction of distance. Time geography explores how human activity is affected by the constraints of movement, especially temporal costs. [11]
In the Euclidean TSP (see below), the distance between two cities is the Euclidean distance between the corresponding points. In the rectilinear TSP, the distance between two cities is the sum of the absolute values of the differences of their x- and y-coordinates. This metric is often called the Manhattan distance or city-block metric.
Ring Road, Vienna, Austria, June 2005 Commuters on the New York City Subway during rush hour Rush hour at Shinjuku Station, Tokyo Traffic jam in Baltimore, Maryland. Commuting is periodically recurring travel between a place of residence and place of work or study, where the traveler, referred to as a commuter, leaves the boundary of their home community. [1]
The gravity model illustrates the macroscopic relationships between places (say homes and workplaces). It has long been posited that the interaction between two locations declines with increasing (distance, time, and cost) between them, but is positively associated with the amount of activity at each location (Isard, 1956).
Headway is the distance or duration between vehicles in a transit system. The minimum headway is the shortest such distance or time achievable by a system without a reduction in the speed of vehicles. The precise definition varies depending on the application, but it is most commonly measured as the distance from the tip (front end) of one ...
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