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Search: MSC category 52C99 ( None of the above, but in this section )

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1. CMB 2010 (vol 53 pp. 394)

 On Nearly Equilateral Simplices and Nearly lâ Spaces By $\textrm{d}(X,Y)$ we denote the (multiplicative) Banach--Mazur distance between two normed spaces $X$ and $Y.$ Let $X$ be an $n$-dimensional normed space with $\textrm{d}(X,\ell_\infty^n) \le 2,$ where $\ell_\infty^n$ stands for $\mathbb{R}^n$ endowed with the norm $\|(x_1,\dots,x_n)\|_\infty := \max \{|x_1|,\dots, |x_n| \}.$ Then every metric space $(S,\rho)$ of cardinality $n+1$ with norm $\rho$ satisfying the condition $\max D / \min D \le 2/ \textrm{d}(X,\ell_\infty^n)$ for $D:=\{ \rho(a,b) : a, b \in S, \ a \ne b\}$ can be isometrically embedded into $X.$ Categories:52A21, 51F99, 52C99
 Geometric Floral'' Configurations With an increase in size, configurations of points and lines in the plane usually become complicated and hard to analyze. The floral'' configurations we are introducing here represent a new type that makes accessible and visually intelligible even configurations of considerable size. This is achieved by combining a large degree of symmetry with a hierarchical construction. Depending on the details of the interdependence of these aspects, there are several subtypes that are described and investigated. Categories:52C30, 52C99