Rational Tangles
نویسندگان
چکیده
منابع مشابه
Classifying and Applying Rational Knots and Rational Tangles
In this survey paper we sketch new combinatorial proofs of the classification of rational tangles and of unoriented and oriented rational knots, using the classification of alternating knots and the calculus of continued fractions. We continue with the classification of achiral and strongly invertible rational links, and we conclude with a description of the relationships among tangles, rationa...
متن کاملOn the classification of rational tangles
In this paper we give two new combinatorial proofs of the classification of rational tangles using the calculus of continued fractions. One proof uses the classification of alternating knots. The other proof uses colorings of tangles. We also obtain an elementary proof that alternating rational tangles have minimal number of crossings. Rational tangles form a basis for the classification of kno...
متن کاملRational Tangles and the Modular Group
There is a natural way to define an isomorphism between the group of transformations of isotopy classes of rational tangles and the modular group. This isomorphism allows to give a simple proof of the Conway theorem, stating the one-to-one correspondence between isotopy classes of rational tangles and rational numbers. Two other simple ways to define this isomorphism, one of which suggested by ...
متن کاملRational Structure on Algebraic Tangles and Closed Incompressible Surfaces in Algebraically Alternating Knots and Links
Let F be an incompressible, meridionally incompressible and not boundary-parallel surface in the complement of an algebraic tangle (B, T ). Then F separates the strings of T in B and the boundary slope of F is uniquely determined by (B, T ) and hence we can define the slope of the algebraic tangle. In addition to the Conway’s tangle sum, we define a natural product of two tangles. The slopes an...
متن کاملTangled Tangles
The Tangle toy [Zaw15, Zaw85] is a topological manipulation toy that can be twisted and turned in a variety of different ways, producing different geometric configurations. Some of these configurations lie in 3D space while others may be flattened into planar shapes. The toy consists of several curved, quarter-circle pieces fit together at rotational/twist joints. Each quarter-circle piece can ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 1997
ISSN: 0196-8858
DOI: 10.1006/aama.1996.0511