Kadets-Type Theorems for Partitions of a Convex Body
For convex partitions of a convex body B, we try to put a homothetic copy of B into each set of the partition so that the sum of the homothety coefficients is at least 1. In the plane this can be done for an arbitrary partition, while in higher dimensions we need certain restrictions on the partition.
the tarski plank problem the kadets theorem