Tiling by squares, Kirchhoff’s laws and a flow problem in the economy

Arkadiusz Maciuk , Antoni Smoluk

Abstract

The problem of tiling by squares was formulated more than one hundred years ago and has been mostly regarded as an interesting mathematical issue in geometry, yet without any special practical associations. In addition to a historical outline of the problem, this paper demonstrates how Smith’s 1940 method using digraphs helps associate an issue linked to two-dimensional dissection or packaging with such economic problems as transportation network planning, researching linkages between suppliers and the like. We also discuss simple perfect squared rectangles whose relevant laws of nature are as yet unknown, according to the principle that elegant scientific structures sooner or later find their equivalents in the real world.
Author Arkadiusz Maciuk (MISaF / IZM / DoMaC)
Arkadiusz Maciuk,,
- Department of Mathematics and Cybernetics
, Antoni Smoluk (WUE)
Antoni Smoluk,,
- Wrocław University of Economics
Journal seriesDidactics of Mathematics, ISSN 1733-7941, (B 8 pkt)
Issue year2017
No14 (18)
Pages33-44
Publication size in sheets0.55
Keywords in Englishsquarings, digraph, Kirchhoff’s laws, flow problem in the economy
DOIDOI:10.15611/dm.2017.14.04
URL https://www.dbc.wroc.pl/dlibra/publication/123352
Languageen angielski
LicenseJournal (articles only); author's original; Uznanie Autorstwa - Użycie Niekomercyjne - Bez utworów zależnych (CC-BY-NC-ND); after publication
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Maciuk_Smoluk_Tiling_by_squares.pdf 259,43 KB
Score (nominal)8
ScoreMinisterial score = 8.0, 20-08-2019, ArticleFromJournal
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