Affine congruence by dissection of discs - appropriate groups and optimal dissections |
| |
Authors: | Christian Richter |
| |
Institution: | 1. Mathematisches Institut, Friedrich-Schiller-Universit?t, D-07737, Jena, Germany
|
| |
Abstract: | Let
be a group of affine transformations of the Euclidean plane
. Two topological discs D,
are called congruent by dissection with respect to
if D can be dissected into a finite number of subdiscs that can be rearranged by maps from
to a dissection of E.
Our main result says in particular that
admits congruence by dissection of any circular disc C with any square S if and only if
contains a contractive map and all orbits
,
, are dense in
. In this case any two discs D and E are congruent by dissection with respect to
and every disc D is congruent by dissection with n copies of D for every n ≥ 2.
Moreover, we give estimates on minimal numbers of pieces that are needed to realize congruences by dissection.
Dedicated to Irmtraud Stephani on the occasion of her 70th birthday |
| |
Keywords: | 52B45 |
本文献已被 SpringerLink 等数据库收录! |
|