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The mathematical study of knots. Knot theory considers questions such as the following: 1. Given a tangled loop of string, is it really knotted or can it, with enough ...

On a measure space X, the set of square integrable L2-functions is an L^2-space. Taken together with the L2-inner product with respect to a measure mu, <f,g>=int_Xfgdmu (1) ...

The Laplacian spectral ratio R_L(G) of a connected graph G is defined as the ratio of its Laplacian spectral radius to its algebraic connectivity. If a connected graph of ...

A path composed of connected horizontal and vertical line segments, each passing between adjacent lattice points. A lattice path is therefore a sequence of points P_0, P_1, ...

Let L=(L, ^ , v ) be a lattice, and let tau subset= L^2. Then tau is a tolerance if and only if it is a reflexive and symmetric sublattice of L^2. Tolerances of lattices, ...

The Lebesgue measure is an extension of the classical notions of length and area to more complicated sets. Given an open set S=sum_(k)(a_k,b_k) containing disjoint intervals, ...

The series for the inverse tangent, tan^(-1)x=x-1/3x^3+1/5x^5+.... Plugging in x=1 gives Gregory's formula 1/4pi=1-1/3+1/5-1/7+1/9-.... This series is intimately connected ...

The Lemoine cubic is the triangle cubic with trilinear equation It passes through Kimberling centers X_n for n=3, 4, 32, 56, and 1147.

The Lester circle is the circle on which the circumcenter C, nine-point center N, and the first and second Fermat points X and X^' lie (Kimberling 1998, pp. 229-230). Besides ...

The set of left cosets of a subgroup H of a topological group G forms a topological space. Its topology is defined by the quotient topology from pi:G->G/H. Namely, the open ...