[HTML][HTML] Answers to questions of Grünbaum and Loewner
S Myroshnychenko, K Tatarko, V Yaskin - Advances in Mathematics, 2025 - Elsevier
We construct a convex body K in R n, n≥ 5, with the property that there is exactly one
hyperplane H passing through c (K), the centroid of K, such that the centroid of K∩ H …
hyperplane H passing through c (K), the centroid of K, such that the centroid of K∩ H …
On the maximal distance between the centers of mass of a planar convex body and its boundary
F Nazarov, D Ryabogin, V Yaskin - Discrete & Computational Geometry, 2024 - Springer
We prove that the length of the projection of the vector joining the centers of mass of a
convex body on the plane and of its boundary to an arbitrary direction does not exceed 1 6 …
convex body on the plane and of its boundary to an arbitrary direction does not exceed 1 6 …
[PDF][PDF] Centers of mass of convex bodies
The research efforts of our team were dedicated to investigation of questions regarding the
mutual positions of various centers of mass in a convex body. First studies of centers of mass …
mutual positions of various centers of mass in a convex body. First studies of centers of mass …