Equilateral triangles in subsets of ℝd of large Hausdorff dimension
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DOI: 10.1007/s11856-019-1848-8
Abstract: We prove that subsets of ℝd, d ≥ 4 of large enough Hausdorff dimensions contain vertices of an equilateral triangle. It is known that additional hypotheses are needed to assure the existence of equilateral triangles… read more here.
Keywords: equilateral triangles; subsets large; triangles subsets; hausdorff dimension ... See more keywords
Some Geometric Constants Related to the Midline of Equilateral Triangles in Banach Spaces
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DOI: 10.3390/sym14020348
Abstract: We will introduce some new geometric constants based on the constant H(X) proposed by Gao and the constant A2(X) proposed by M. Baronti et al. We first provide a study of a new constant M1(X)… read more here.
Keywords: related midline; equilateral triangles; midline equilateral; constants related ... See more keywords