**Original Paper**

# Approximation of convex bodies by inscribed simplices of maximum volume

## Authors

- First online:
- Received:

DOI: 10.1007/s13366-011-0026-x

## Abstract

The Banach-Mazur distance between an arbitrary convex body and a simplex in Euclidean *n*-space *E*
^{
n
} is at most *n* + 2. We obtain this estimate as an immediate consequence of our theorem which says that for an arbitrary convex body *C* in *E*
^{
n
} and for any simplex *S* of maximum volume contained in *C* the homothetical copy of *S* with ratio *n* + 2 and center in the barycenter of *S* contains *C*. In general, this ratio cannot be improved, as it follows from the example of any double-cone.

### Keywords

Approximation Banach–Mazur distance Convex body Double-cone Simplex Volume### Mathematics Subject Classification (2000)

52A21 52A10 46B20## Open Access

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