We indicate a few properties of equilateral sets in normed spaces, mainly with respect to some of their ‘central’ points (centers, medians, barycenters). In particular, we show that we have an extremely simple situation only when the norm springs from an inner product. By means of examples, dealing mainly with equilateral triangles, we describe in detail the different situations that may occur.
Equilateral sets and their central points
CASINI, EMANUELE GIUSEPPE;
1993-01-01
Abstract
We indicate a few properties of equilateral sets in normed spaces, mainly with respect to some of their ‘central’ points (centers, medians, barycenters). In particular, we show that we have an extremely simple situation only when the norm springs from an inner product. By means of examples, dealing mainly with equilateral triangles, we describe in detail the different situations that may occur.
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