  Let $M$ be the space of triangles, defined up to shifts, rotations and
dilations. We define two maps $f:M\to M$ and $g:M\to M$. The map $f$
corresponds to a triangle of perimeter $\pi$ the triangle with angles
numerically equal to edges of the initial triangle. The map $g$ corresponds to
a triangle of perimeter $2\pi$ the triangle with \emph{exterior} angles
numerically equal to edges of the initial triangle. For $p\in M$ the sequence
$\{p,f(p),f(f(p)),\ldots\}$ converges to the equilateral triangle and the
sequence $\{p,g(p),g(g(p)),\ldots\}$ converges to the "degenerate triangle"
with angles $(0,0,\pi)$. In Supplement an analogous problem about
inscribed-circumscribed quadrangles is discussed.
