Menasco's Theorem
For a Braid with 
strands, 
components, 
positive crossings, and 
negative crossings,
where
are the smallest number of positive and negative crossings which must be changed to crossings of the oppositesign. These inequalities imply Bennequin's Conjecture. Menasco's theorem can be extended to arbitrary knot diagrams.See also Bennequin's Conjecture, Braid, Unknotting Number
References
Cipra, B. ``From Knot to Unknot.'' What's Happening in the Mathematical Sciences, Vol. 2. Providence, RI: Amer. Math. Soc., pp. 8-13, 1994. Menasco, W. W. ``The Bennequin-Milnor Unknotting Conjectures.'' C. R. Acad. Sci. Paris Sér. I Math. 318, 831-836, 1994.
- Resultant
- Retardance
- Reuleaux Polygon
- Reuleaux Triangle
- Reversal
- Reverse Greedy Algorithm
- Reverse-Then-Add Sequence
- Reversion of Series
- Reznik's Identity
- Rhodonea
- Rhomb
- Rhombic Dodecahedral Number
- Rhombic Dodecahedron
- Rhombic Icosahedron
- Rhombicosacron
- Rhombicosahedron
- Rhombicosidodecahedron
- Rhombic Polyhedron
- Rhombic Triacontahedron
- Rhombicuboctahedron
- Rhombidodecadodecahedron
- Rhombihexacron
- Rhombihexahedron
- Rhombitruncated Cuboctahedron
- Rhombitruncated Icosidodecahedron