Congruence by dissection of convex discs via similarities

Preprint series: 01-07, Reports on Algebra and Geometry

MSC:
52B45 Dissections and valuations (Hilbert's third problem, etc.)
52A10 Convex sets in $2$ dimensions (including convex curves), See also {53A04}

Abstract: We show that any two convex discs $D,E \subseteq {\mathbb R}^2$ are congruent by dissection with respect to
the group ${\mathcal S}^+$ of proper similarities such that
only three topological discs with rectifiable boundary are
used as pieces of dissection. In general, two pieces of
dissection do not suffice.

Keywords: congruence by dissection, similarity, homothety, convex disc, squaring the circle