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A string figure is any pattern produced when a looped string is spanned between two hands and is twisted and woven in various manners around the fingers and the wrists. The ...

A prime link is a link that cannot be represented as a knot sum of other links. Doll and Hoste (1991) list polynomials for oriented links of nine or fewer crossings, and ...

A hole in a mathematical object is a topological structure which prevents the object from being continuously shrunk to a point. When dealing with topological spaces, a ...

A general plane quartic curve is a curve of the form (1) Examples include the ampersand curve, bean curve, bicorn, bicuspid curve, bifoliate, bifolium, bitangent-rich curve, ...

There are many unsolved problems in mathematics. Several famous problems which have recently been solved include: 1. The Pólya conjecture (disproven by Haselgrove 1958, ...

Any nondegenerate closed space curve may be nondegenerately deformed into either of the two curves illustrated above. Neither of these can be nondegenerately transformed into ...

A type II Markov move.

The Reidemeister move of type I.

The Conway polynomial del _L(x), sometimes known as the Conway-Alexander polynomial, is a modified version of the Alexander polynomial Delta_L(x) that was formulated by J. H. ...

Let L be a link in R^3 and let there be a disk D in the link complement R^3-L. Then a surface F such that D intersects F exactly in its boundary and its boundary does not ...