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• # Artykuł - szczegóły

## Colloquium Mathematicum

2015 | 138 | 2 | 205-216

## Reduced spherical polygons

EN

### Abstrakty

EN
For every hemisphere K supporting a spherically convex body C of the d-dimensional sphere $S^{d}$ we consider the width of C determined by K. By the thickness Δ(C) of C we mean the minimum of the widths of C over all supporting hemispheres K of C. A spherically convex body $R ⊂ S^{d}$ is said to be reduced provided Δ(Z) < Δ(R) for every spherically convex body Z ⊂ R different from R. We characterize reduced spherical polygons on S². We show that every reduced spherical polygon is of thickness at most π/2. We also estimate the diameter of reduced spherical polygons in terms of their thickness. Moreover, a few other properties of reduced spherical polygons are given.

205-216

wydano
2015

### Twórcy

autor
• Institute of Mathematics and Physics, University of Science and Technology, 85-789 Bydgoszcz, Poland