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Let Delta denote an integral convex polytope of dimension n in a lattice M, and let l_Delta(k) denote the number of lattice points in Delta dilated by a factor of the integer ...

The elongated square gyrobicupola nonuniform polyhedron obtained by rotating the bottom third of a small rhombicuboctahedron (Ball and Coxeter 1987, p. 137). It is also ...

A transformation of the form w=f(z)=(az+b)/(cz+d), (1) where a, b, c, d in C and ad-bc!=0, (2) is a conformal mapping called a linear fractional transformation. The ...

The Miller Institute knot is the 6-crossing prime knot 6_2. It is alternating, chiral, and invertible. A knot diagram of its laevo form is illustrated above, which is ...

Define q=e^(2piitau) (cf. the usual nome), where tau is in the upper half-plane. Then the modular discriminant is defined by ...

The perspective image of an infinite checkerboard. It can be constructed starting from any triangle DeltaOXY, where OX and OY form the near corner of the floor, and XY is the ...

A right strophoid is the strophoid of a line L with pole O not on L and fixed point O^' being the point where the perpendicular from O to L cuts L is called a right ...

Rule 28 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

The Siegel theta function is a Gamma_n-invariant meromorphic function on the space of all p×p symmetric complex matrices Z=X+iY with positive definite imaginary part. It is ...

A smooth structure on a topological manifold (also called a differentiable structure) is given by a smooth atlas of coordinate charts, i.e., the transition functions between ...