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The view-obstruction problem for spheres in ℝ5

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Abstract

In the view-obstruction problem, congruent, closed convex bodies centred at the points\(\frac{1}{2},{\text{ }}...{\text{ , }}\frac{{\text{1}}}{{\text{2}}} + \mathbb{Z}^n \) in ℝn are expanded uniformly until they block all rays from the origin into the open positive cone. The central problem is to determine the minimal blocking size. In the case of spheres of diameter 1 and cubes of side 1 these values are known forn=2, 3 and 4. Here we show that in ℝ5, this value for the sphere of diameter 1 is\(\sqrt {41/42} \).

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Authors and Affiliations

  1. Centre for Advanced Study in Mathematics, Panjab University, 160014, Chandigarh, India

    V. C. Dumir & R. J. Hans-Gill

  2. Physical Sciences Division Scarborough College, University of Toronto, M1C 1A4, Scarborough, Ontario, Canada

    J. B. Wilker

Authors
  1. V. C. Dumir
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  2. R. J. Hans-Gill
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  3. J. B. Wilker
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Dumir, V.C., Hans-Gill, R.J. & Wilker, J.B. The view-obstruction problem for spheres in ℝ5 . Monatshefte für Mathematik 122, 21–34 (1996). https://doi.org/10.1007/BF01298453

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  • DOI: https://doi.org/10.1007/BF01298453

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