We introduced concept of meander knots, 2-component meander links and multi-component meander links and derived different families of meander knots and links from open meanders with n ? 16 crossings. We also defined semi-meander knots (or knots with ordered Gauss code) and their product.

We analyze adequacy of knots and links, utilizing Conway notation, Montesinos tangles and Linknot and KhoHo computer calculations. We introduce a numerical invariant called adequacy number, and compute adequacy polynomial which is the invariant of alternating link families. According to computational results, adequacy polynomial distinguishes (up to mutation) all families of alternating knots and links generated by links with at most 12 crossings.

We analyze applications of knots and links in the Ancient art, beginning from Babylonian, Egyptian, Greek, Byzantine and Celtic art. Construction methods used in art are analyzed on the examples of Celtic art and ethnical art of Tchokwe people from Angola or Tamil art, where knots are constructed as mirror-curves. We propose different methods for generating knots and links based on geometric polyhedra, suitable for applications in architecture and sculpture.

For any link and for any modulus $m$ we introduce an equivalence relation on the set of non-trivial $m$-colorings of the link (an $m$-coloring has values in $\mathbf{Z}/m\mathbf{Z}$). Given a diagram of the link, the equivalence class of a non-trivial $m$