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The notion of parallel transport on a manifold M makes precise the idea of translating a vector field V along a differentiable curve to attain a new vector field V^' which is ...

The term "parameter" is used in a number of ways in mathematics. In general, mathematical functions may have a number of arguments. Arguments that are typically varied when ...

A linkage with six rods which draws the inverse of a given curve. When a pencil is placed at P, the inverse is drawn at P^' (or vice versa). If a seventh rod (dashed) is ...

Define a pebbling move as a transer of two pebbles from one vertex of a graph edge to an adjacent vertex with one of the pebbles being removed in transit as a toll. The ...

An impossible figure in which a stairway in the shape of a square appears to circulate indefinitely while still possessing normal steps (Penrose and Penrose 1958). The Dutch ...

The pentagonal hexecontahedron is the 60-faced dual polyhedron of the snub dodecahedron A_8 (Holden 1971, p. 55). It is Wenninger dual W_(18). A tetrahedron 10-compound, cube ...

The pentagonal icositetrahedron is the 24-faced dual polyhedron of the snub cube A_7 and Wenninger dual W_(17). The mineral cuprite (Cu_2O) forms in pentagonal ...

A perfect power is a number n of the form m^k, where m>1 is a positive integer and k>=2. If the prime factorization of n is n=p_1^(a_1)p_2^(a_2)...p_k^(a_k), then n is a ...

A pair of elements (p_i,p_j) is called an inversion in a permutation p if i>j and p_i<p_j (Skiena 1990, p. 27; Pemmaraju and Skiena 2003, p. 69). For example, in the ...

A set of ascending sequences in a permutation is called a run (Graham et al. 1994) or sometimes a rise (Comtet 1974, p. 241). A sorted permutation consists of a single run, ...