by **
C. Richter**

**Preprint series:** 02-02, Reports on Algebra and Geometry

**Preprint series:**
, Reports on Algebra and Geometry

**MSC:**- 52B45 Dissections and valuations (Hilbert's third problem, etc.)

**Abstract:** Let $\mathcal G$ be a group of affine

transformations of the plane that contains a strict

contraction and all translations. It is shown that any

two topological discs $D,E \subseteq {\mathbb R}^2$

are congruent by dissection with respect to

$\mathcal G$ such that only three topological discs

are used as pieces of dissection. Two pieces of

dissection do not suffice in general even if

$\mathcal G$ consists of all affine transformations.

**Keywords:** *Congruence by dissection, topological disc, minimal number of pieces, homothety, similarity, affine map, Tarski's circle squaring problem.*

**Upload:** 2002
-06
-12

**Update:** 2002
-06
-12

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