 About 5,760 results  books.google.com 
 books.google.com Remark 22.1.4 This example suggests the following question: If we assume
Archimedes' axiom (A) in addition, are the notions of equidecomposable and
equal content equivalent? We will see that the answer is yes in any Hilbert plane
with (P) ... 

 books.google.com We shall now begin to examine the problems of equidecomposability and
equicomplementabilityforsolid bodies (polyhedra). Two polyhedra are said to be
equidecomposable if one of them can be decomposed into a finite number of
parts in ... 

 books.google.com ... set of functions 4A2A, 465Xj equidecomposable (in 'Gequidecomposable')
396Ya; (in 'Grequidecomposable') §395 (395 A); (in 'Gcrequide composable')
§448 (448A) equidistributed sequence (in a topological probability space) 281N,
... 

 books.google.com 
 books.google.com We show that any two rectangles of the same area are equidecomposable using
translations alone. It is clear that a rectangle of size a x b is equidecomposable to
a rectangle of size (a/2) x (26) using two pieces and translations. Repeating this ... 

 books.google.com any two countably infinite sets of X are countably Gequidecomposable. In
particular, any countably infinite subset of X is countably Gparadoxical. Exercise
2.2.1. Show that finite Gequidecomposability and countable G
equidecomposability ... 

 books.google.com Gardner's Theorem 8.1. Indeed. suppose that D and Q are equidecomposable
using the translations t,t3, t3. Replacing D by n (D) we may assume that t] is the
identity. Then t1, t2, t3 generate a discrete group. which contradicts Theorem 8.1. 

 books.google.com 7s a regular tetrahedron in R3 equidecomposable to a cube using Lebesgue
measurable pieces ? We may add the following question posed by the author in
Section 10.2 of [23]. Problem 6.3. Is every polygon equidecomposable to a
square ... 

 books.google.com Paradoxical Sets Suppose that the group G acts on the set X. A subset A of X is G
paradoxical, or simply paradoxical, if it is equal to A1 ∪A2 for some pair A1, A2
of disjoint subsets of A, each of which is Gequidecomposable with A. The ... 

 