On-line covering the unit square with squares

• Autorzy: Januszewski, J.
• Języki publikacji: EN

Abstrakty

EN

The unit square can be on-line covered with any sequence of squares whose total area is not smaller than 4.

Słowa kluczowe

EN

on-line covering; square

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: Vol. 57, no 1
• Strony: 57-62
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Januszewski, J.

• Institute of Mathematics and Physics, University of Technology and Life Sciences, Kaliskiego 7 85-796 Bydgoszcz, Poland,

Bibliografia

• [1] H. Groemer, Covering and packing by sequences of convex sets, in: Discrete Geometry and Convexity, Ann. New York Acad. Sci. 440, 1985, 262-278.
• [2] B. Grünbaum, Measures of symmetry of convex sets, in: Convexity, Proc. Sympos. Pure Math. 7, Amer. Math. Soc., Providence, 1963, 233-270.
• [3] J. Januszewski and M. Lassak, On-line covering the unit cube by cubes, Discrete Comput. Geom. 12 (1994), 433-438.
• [4] J. Januszewski and M. Lassak, On-line covering the unit square by squares and the three-dimensional unit cube by cubes, Demonstratio Math. 28 (1995), 143-149.
• [5] J. Januszewski, M. Lassak, G. Rote and G. Woeginger, On-line q-adic covering by the method of the n-th segment and its application to on-line covering by cubes, Beiträge Algebra Geom. 37 (1996), 51-65.
• [6] W. Kuperberg, On-line covering a cube by a sequence of cubes, Discrete Comput. Geom. 12 (1994), 83-90.
• [7] M. Lassak, A survey of algorithms for on-line packing and covering by sequences of convex bodies, Bolyai Soc. Math. Stud. 6, Janos Bolyai Math. Soc., Budapest, 1997, 129-157.
• [8] J. W. Moon and L. Moser, Some packing and covering theorems, Colloq. Math. 17 (1967), 103-110.