Pseudotilings, or why is a raven like a writing-desk
Gaiane Panina

Two* problems will be explained to have one and the same  clue.

1. Carpenter's problem.
Can any carpenter's ruler (a planar non-crossing closed broken line)
be straightened in the plane without self-crossing?

2. A.D. Alexandrov's problem.
Given a smooth convex 3D-body K and a constant C
which separates the principal curvature radii of K
(i.e. R1 \leq C \leq R2 everywhere),
is K necessarily a ball?

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* well... much  more than just two!