Dihedral f-tilings of the sphere by equilateral and scalene triangles. III.

D'Azevedo Breda, A.M.; Ribeiro, Patrícia S.; Santos, Altino F.

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Dihedral $f$ -tilings of the sphere by equilateral and scalene triangles. II.

d&amp;#039;Azevedo Breda, A.M., Ribeiro, Patrícia S., Santos, Altino F. (2008)

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Large dimensional sets not containing a given angle

Viktor Harangi (2011)

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We say that a set in a Euclidean space does not contain an angle α if the angle determined by any three points of the set is not equal to α. The goal of this paper is to construct compact sets of large Hausdorff dimension that do not contain a given angle α ∈ (0,π). We will construct such sets in ℝn of Hausdorff dimension c(α)n with a positive c(α) depending only on α provided that α is different from π/3, π/2 and 2π/3. This improves on an earlier construction (due to several authors)...