Acta mathematica scientia,Series B ›› 2002, Vol. 22 ›› Issue (2): 189-198.

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ILLUMINATION AND EXPOSITION OF A CONVEX n-DIMENSIONAL BODY DEPENDING ON ITS SHARPNESS

 Boris V. Dekster   

  1. Mathematics, Mount Allison University, Sackville, N.B. E0A 3C0, Canada
  • Online:2002-04-15 Published:2002-04-15

Abstract:

A convex n-body C is said to be exposable to a set D of a few directions if there is a linear transformation L : En ! En such that L(C) and each body isometric to L(C) is illuminated by D. Denote by En the minimum integer such that each C is exposable to a (fixed) set D of cardinality En. An upper bound for En is established here.

Key words: Covering, illumination, Hadwiger conjecture

CLC Number: 

  • 52C17
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