Translative packing of unit squares into equilateral triangles

• Autorzy: Januszewski J.

Identyfikatory

DOI

10.1515/dema-2015-0032

• Języki publikacji: EN

Abstrakty

EN

Every collection of n (arbitrary-oriented) unit squares can be packed translatively into any equilateral triangle of side length 2.3755 ∙ √n.

Słowa kluczowe

EN

packing; translative packing; triangle

PL

pakowanie; trójkąt

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2015
• Tom: Vol. 48, nr 3
• Strony: 452--461
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Januszewski J.

• Institute of Mathematics and Physics, University of Technology and Life Sciences, Al. Prof. S. Kaliskiego 7, 85-789 Bydgoszcz, Poland

Bibliografia

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• [2] G. Fejes-Tóth, Packing and covering, in: Handbook of Discrete and Computational Geometry, J. E. Goodman, J. O’Rourke, eds., 1997, 19–41.
• [3] E. Friedman, Packing unit squares in squares: a survey and new results, Electron. J. Combin., Dynamic Survey 7, 2000.
• [4] F. Göbel, Geometrical packing and covering problems, in: Packing and Covering in Combinatorics, A. Schrijver, ed., Math. Centrum Tracts 106 (1979), 179–199.
• [5] H. Groemer, Covering and packing properties of bounded sequences of convex sets, Mathematica 29 (1982), 18–31.
• [6] J. Januszewski, Translative packing of unit squares into squares, International Journal of Mathematics and Mathematical Sciences, Volume 2012 (2012), Article ID 613201, 7 pages, doi:10.1155/2012/613201.
• [7] J. Januszewski, Translative covering by unit squares, Demonstratio Math. 46(3) (2013), 605–616.
• [8] H. Melissen, Densest packings of congruent circles in an equilateral triangle, Amer. Math. Monthly 100(10) (1993), 916–925.
• [9] N. Oler, A finite packing problem, Canad. Math. Bull. 4 (1961), 153–155.