Tiling by Squares, Kirchhoff's Laws and a Flow Problem in the Economy

• Autorzy: Arkadiusz Maciuk , Antoni Smoluk
• Języki publikacji: EN

Abstrakty

EN

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.(original abstract)

Słowa kluczowe

EN

Mathematics; Quantitative methods

PL

Matematyka; Metody ilościowe

• Czasopismo: Didactics of Mathematics
• Rocznik: 2017
• Numer: nr 14 (18)
• Strony: 33--44

Twórcy

autor

Arkadiusz Maciuk

• Wrocław University of Economics, Poland

autor

Antoni Smoluk

• Wrocław University of Economics, Poland

Bibliografia

• Anderson S. (2016). Squaring.Net. http://www.squaring.net/.
• Brooks R.L., Smith C.A., Stone A.H., Tutte W.T. (1940). The dissection of rectangles into squares. Duke Mathematical Journal. No. 7. Pp. 213-340.
• Dehn M. (1903). Über Zerlegung von Rechtecken in Rechtecke. Math. Annalen. No. 57. Pp. 314-332.
• Duijvestijn A.J.W. (1978). Simple perfect square of lowest order. Journal of Combinational Theory. Ser. B. No. 25. Pp. 240-243.
• Kurz S. (2012). Squaring the square with integer linear programming. Journal of Information Processing. No. 20(3). Pp. 680-685.
• Moroń Z. (1925). O rozkładach prostokątów na kwadraty. Przegląd Matematyczno-Fizyczny. No. 3. Pp. 152-153.
• Moroń Z. (1955). O rozkładach prostokątów na nierówne kwadraty. Wiadomości Matematyczne. No. 1(1). Pp. 75-94.
• Sprague R. (1939). Beispiel einer Zerlegung des Quadrats in lauter verschiedene Quadrate, Mathematische Zeitschrift. No. 45. Pp. 607-608.

Identyfikatory

DOI

10.15611/dm.2017.14.04