Year: 2025
Type: article
Abstract: Steinitz’s theorem states that if the origin belongs to the interior of the convex hull of a set $$Q \subset {\mathbb {R}}^d,$$ Q ⊂ R d , then there are at most 2d points $$Q^\prime $$ Q ′ of Q whose convex hull contains the origin in the interior. Bárány, Katchalski and Pach gave a quantitative version, whereby the radius of the ball contained in the convex hull of $$Q^\prime $$ Q ′ is bounded from below. In the present note, we show that a Euclidean result of this kind implies a corresponding spherical version.
Authors: Grigory Ivanov, Márton Naszódi
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4407765539