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Weber problem

In geometry, the Weber problem, named after Alfred Weber, is one of the most famous problems in location theory. It requires finding a point in the plane that minimizes the sum of the transportation costs from this point to n destination points, where different destination points are associated with different costs per unit distance.

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Definition and history of the Fermat, Weber, and attraction-repulsion problems

Pierre de FermatTohoku Mathematical journalLuc-Normand TellierThomas Simpson
4 related topics

The attraction–repulsion problem and the New Economic Geography

New Economic GeographyPaul KrugmanNobel Memorial Prize in Economic SciencesCentripetal force
4 related topics

Iterative solutions of the Fermat, Weber and attraction-repulsion problems

Iteratively reweighted least squaresWeiszfeld's algorithmVarignon frame
3 related topics

Torricelli’s geometrical solution of the Fermat triangle problem

Evangelista TorricelliEuclidean geometry
2 related topics

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Overview

Definition and history of the Fermat, Weber, and attraction-repulsion problems

Torricelli’s geometrical solution of the Fermat triangle problem

Iterative solutions of the Fermat, Weber and attraction-repulsion problems

Interpretation of the land rent theory in the light of the attraction–repulsion problem

The attraction–repulsion problem and the New Economic Geography

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Map overview Semantic statistics

Weber problem

Nodes27
Edges26
Triples124
Avg. degree1.93
Density0.074074
Components1

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Weber problem

Top relations

related to References · 76
Weber problem → Alfred, An Efficient Algorithm, Annexe, Application, Attraction, Boris Polanski, Brigitte, Chen, Chicago, Chicago University Press, Chicoutimi, Christophe Meyer, Different Solution Types, Dynamic Processes, English, Environment, Extension, Fluxions, Frequency, Gaëtan Morin
related to history · 21
Weber problem → Alfred Weber, As, Fermat, Fermat-Weber, French, In, It, Kuenne, Kuenne's, Kuhn, Pierre, Tellier, Tellier's, The Weber, Thomas Simpson, Tohoku Mathematical, Torricelli, USA, Vaszoni, Weber
related to Iterative solutions of the Fermat, Weber and attraction-repulsion problems · 12
Weber problem → As, Fermat, Geometric, In, Iterative, Kuenne, Kuhn, The Varignon, Their, Weber, Weiszfeld's, When
related to Tellier’s trigonometric solution of the triangle attraction-repulsion problem · 10
Weber problem → A1, A2, Determine, Fermat, Here, Let, So, Tellier, Tellier's, Weber
related to External links · 4
Weber problem → EMS Press, Encyclopedia, Mathematics, Weber
is a · 1
Weber problem → generalization of the Fermat problem since it involves both equal and unequal attractive forces

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Important terminology

problem weber solution triangle three fermat point points forces location case tellier attraction attractive angles one must two geometrical repulsion

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Weber problemis ageneralization of the Fermat problem since it involves both equal and unequal attractive forces0.90text
Weber problemrelated to External linksWeber0.60section
Weber problemrelated to External linksEncyclopedia0.60section
Weber problemrelated to External linksMathematics0.60section
Weber problemrelated to External linksEMS Press0.60section
Weber problemrelated to historyIn0.60section
Weber problemrelated to historyFermat0.60section
Weber problemrelated to historyIt0.60section
Weber problemrelated to historyFrench0.60section
Weber problemrelated to historyPierre0.60section
Weber problemrelated to historyTorricelli0.60section
Weber problemrelated to historyWeiszfeld0.60section

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