Search: MSC category 52A15 ( Convex sets in $3$ dimensions (including convex surfaces) [See also 53A05, 53C45] )
 Shaken Rogers's Theorem for Homothetic Sections We shall prove the following shaken Rogers's theorem for homothetic sections: Let $K$ and $L$ be strictly convex bodies and suppose that for every plane $H$ through the origin we can choose continuously sections of $K$ and $L$, parallel to $H$, which are directly homothetic. Then $K$ and $L$ are directly homothetic. Keywords:convex bodies, homothetic bodies, sections and projections, Rogers's TheoremCategory:52A15