 About 20,500 results  books.google.com 
 books.google.com As an application of the previous theorem we shall prove that a rectangle can be
decomposed into finitely many nonoverlapping ... Therefore, by our previous
theorem, b/a is rational. ... The basic idea of the proof of Dehn's theorem is
familiar. 

 books.google.com We will call this more general result the DehnThurston Theorem and will derive
the analogue of this theorem in the setting of train tracks in Theorem 3.1.1. The
remainder of this section is devoted to a discussion of Dehn's Theorem itself; ... 

 books.google.com So in the proofs of both the loop theorem and Dehn's lemma, covering spaces
are used to select the switches that are to be performed, on C and D0,
respectively. As Papakyriakopoulos says of the proof of Dehn's lemma: Actually,
looking ... 

 books.google.com There is a similar but simpler rational independence theorem for the tensor
product R®(R discussed in the previous set of ... Dehn's theorem The regular
tetrahedron is not equidecomposable irith the cube Proof If a is a rational multiple
of n ... 

 books.google.com Thus, Dehn's theorem reduces the trivial link recognition problem to the free
group recognition problem (for some class of groups). In the general case, the
free group recognition problem is undecidable. For more details see [Bir] and [BZ]
. 

 books.google.com By this exercise and the existence and the uniqueness theorems for connected
sum decompositions, we can say that irreducible 3manifolds are fundamental
objects in the study of 3manifold topology. C.2 Dehn's lemma and the loop and ... 

 books.google.com CHAPTER 4 THE LOOP AND SPHERE THEOREMS In 1910, M. Dehn gave a "
proof" [17] of a theorem which has become known as 4.1. DEHN'S LEMMA.
Suppose M is a 3manifold and f : B2 . M is a map such that for some
neighborhood A ... 

 books.google.com SCISSORSCONGRUENCE OF POLYHEDRA AND DEHN'S THEOREM 111 The
problem we are discussing here is called Hilbert's Third Problem. In the same
year (1900), soon after Hilbert presented the problem, his student Max Dehn ... 

 books.google.com The curves viewed in their entirety form a grid like graph paper which gives
global integral coordinates. 0 Theorem 1.4.1 0 1.5. Max Dehn's contribution.
Theorem 1.5.1 (Dehn). Let R denote a rectangle that can be tiled by squares.
Then, if H is ... 

 