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The set of fixed points which do not move as a knot is transformed into itself is not a knot. The conjecture was proved in 1978 (Morgan and Bass 1984). According to Morgan ...

The thin plate spline is the two-dimensional analog of the cubic spline in one dimension. It is the fundamental solution to the biharmonic equation, and has the form ...

Wolfram (2002, p. 123) considered the sequence related to the Collatz problem obtained by iterating w_n={3/2w_(n-1) for w_(n-1) even; 3/2(w_(n-1)+1) for w_(n-1) odd (1) ...

van der Waerden's theorem is a theorem about the existence of arithmetic progressions in sets. The theorem can be stated in four equivalent forms. 1. If N=C_1 union C_2 union ...

An xyz embedding, also called an "xyz drawing," is a three-dimensional embedding such that every axis-parallel line contains either zero or two vertices. Such an embedding is ...

Given any tree T having v vertices of vertex degrees of 1 and 3 only, form an n-expansion by taking n disjoint copies of T and joining corresponding leaves by an n-cycle ...

An elliptic curve is the set of solutions to an equation of the form y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6. (1) By changing variables, y->2y+a_1x+a_3, assuming the field ...

Eigenvectors are a special set of vectors associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic vectors, ...

A one-person game played on a rectangular lattice of lamps which can be turned on and off. A move consists of flipping a "switch" inside one of the squares, thereby toggling ...

Stellation is the process of constructing polyhedra by extending the facial planes past the polyhedron edges of a given polyhedron until they intersect (Wenninger 1989). The ...