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An additive group is a group where the operation is called addition and is denoted +. In an additive group, the identity element is called zero, and the inverse of the ...

Power formulas include sin^2x = 1/2[1-cos(2x)] (1) sin^3x = 1/4[3sinx-sin(3x)] (2) sin^4x = 1/8[3-4cos(2x)+cos(4x)] (3) and cos^2x = 1/2[1+cos(2x)] (4) cos^3x = ...

A fusene is a simple planar 2-connected graph embedded in the plane with all vertices of degree 2 or 3, all bounded faces (not necessarily regular) hexagons, and all vertices ...

In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 ...

For 2<=n<=32, it is possible to select 2n lattice points with x,y in [1,n] such that no three are in a straight line (where "straight line" means any line in the plane--not ...

In the field of percolation theory, the term percolation threshold is used to denote the probability which "marks the arrival" (Grimmett 1999) of an infinite connected ...

Yahtzee is a game played with five 6-sided dice. Players take turns rolling the dice, and trying to get certain types of rolls, each with an assigned point value, as ...

Number Theory

Baxter's four-coloring constant for a triangular lattice is given by C^2 = product_(j=1)^(infty)((3j-1)^2)/((3j-2)(3j)) (1) = 3/(4pi^2)Gamma^3(1/3) (2) = 1.46099848... (3) ...

A square matrix is called bisymmetric if it is both centrosymmetric and either symmetric or antisymmetric (Muir 1960, p. 19).