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A quartic symmetric graph on 30 nodes and 60 edges corresponding to the skeleton of the Archimdean icosidodecahedron, great dodecahemidodecahedron, great icosidodecahedron, ...

A magic hexagon of order n is an arrangement of close-packed hexagons containing the numbers 1, 2, ..., H_(n-1), where H_n is the nth hex number such that the numbers along ...

A cusp is a point at which two branches of a curve meet such that the tangents of each branch are equal. The above plot shows the semicubical parabola curve x^3-y^2=0, which ...

The paradox of a man who states "I am lying." If he is lying, then he is telling the truth, and vice versa. Another version of this paradox is the Epimenides paradox. Such ...

Tarski's theorem says that the first-order theory of reals with +, *, =, and > allows quantifier elimination. Algorithmic quantifier elimination implies decidability assuming ...

The mathematical study of how given quantities can be approximated by other (usually simpler) ones under appropriate conditions. Approximation theory also studies the size ...

Let {f_n(x)} be a sequence of analytic functions regular in a region G, and let this sequence be uniformly convergent in every closed subset of G. If the analytic function ...

Write the exact powers of 2 and 3 in sorted order as 1, 2, 3, 4, 8, 9, 16, 27, 32, ... (OEIS A006899), and let u_n be the nth term in the sequence. Then u_(n+1)-u_n tends to ...

A powerful numerical integration technique which uses k refinements of the extended trapezoidal rule to remove error terms less than order O(N^(-2k)). The routine advocated ...

The first solution to Lamé's differential equation, denoted E_n^m(x) for m=1, ..., 2n+1. They are also called Lamé functions. The product of two ellipsoidal harmonics of the ...