--- res: bibo_abstract: - 'In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by P. Erdős: Given a family of (round) disks of radii r1, … , rn in the plane, it is always possible to cover them by a disk of radius R= ∑ ri, provided they cannot be separated into two subfamilies by a straight line disjoint from the disks. In this note we show that essentially the same idea may work for different analogues and generalizations of their result. In particular, we prove the following: Given a family of positive homothetic copies of a fixed convex body K⊂ Rd with homothety coefficients τ1, … , τn> 0 , it is always possible to cover them by a translate of d+12(∑τi)K, provided they cannot be separated into two subfamilies by a hyperplane disjoint from the homothets.@eng' bibo_authorlist: - foaf_Person: foaf_givenName: Arseniy foaf_name: Akopyan, Arseniy foaf_surname: Akopyan foaf_workInfoHomepage: http://www.librecat.org/personId=430D2C90-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-2548-617X - foaf_Person: foaf_givenName: Alexey foaf_name: Balitskiy, Alexey foaf_surname: Balitskiy - foaf_Person: foaf_givenName: Mikhail foaf_name: Grigorev, Mikhail foaf_surname: Grigorev bibo_doi: 10.1007/s00454-017-9883-x bibo_issue: '4' bibo_volume: 59 dct_date: 2018^xs_gYear dct_identifier: - UT:000432205500011 dct_isPartOf: - http://id.crossref.org/issn/01795376 - http://id.crossref.org/issn/14320444 dct_language: eng dct_publisher: Springer@ dct_title: On the circle covering theorem by A.W. Goodman and R.E. Goodman@ ...