About 5,960 results
|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) ...
|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 ...
Miklós Laczkovich - 2001 - Preview
|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 ...
|9c = 4>c if c C (Joe u sup a2„ \ a2n+i , neti = ip~1cifcC supa2n+i \ a2n+2- neti By |
394Be, 9 G G*, so a and b are G-r-equidecomposable. (c) This is easy to prove
directly from the results in 394B, but also follows at once from (b-i); any transitive
|any two countably infinite sets of X are countably G-equidecomposable. In |
particular, any countably infinite subset of X is countably G-paradoxical. Exercise
2.2.1. Show that finite G-equidecomposability and countable G-
|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.
|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 . Problem 6.3. Is every polygon equidecomposable to a
|Then A − A 1is equidecomposable witha subset of A (it is asubset ofA ), and A is |
equidecomposable with asubset of A − A 1 , namely with A 2. Thus PropositionG.
2 implies thatA and A − A 1 are equidecomposable, andsoA1 and A−A 1form the
|A bounded set is Jordan measurable if and only if its boundary has Jordan |
measure zero if and only if its characteristic function is Riemann integrable (see
Appendix B). Define equidecomposability in 3t„ using the join operation (A v B e
3tv if A ...