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In statistical mechanics, the two-dimensional Ising model is a popular tool used to study the dipole moments of magnetic spins. The Ising model in two dimensions is a type of ...

An extended rooted binary tree satisfying the following conditions: 1. Every node has two children, each colored either red or black. 2. Every tree leaf node is colored ...

The central binomial coefficient (2n; n) is never squarefree for n>4. This was proved true for all sufficiently large n by Sárkőzy's theorem. Goetgheluck (1988) proved the ...

Chebyshev noticed that the remainder upon dividing the primes by 4 gives 3 more often than 1, as plotted above in the left figure. Similarly, dividing the primes by 3 gives 2 ...

The plane figure formed by a sequence of circles C_1, C_2, C_3, ... that are all tangent to each other at the same point and such that the sequence of radii converges to ...

A hedgehog is an envelope parameterized by its Gauss map (Martinez-Maure 1996). Viewed another way, a hedgehog is a Minkowski difference of a convex body (Martinez-Maure ...

If the square is instead erected internally, their centers form a triangle DeltaI_AI_BI_C that has (exact) trilinear vertex matrix given by (1) (E. Weisstein, Apr. 25, 2004). ...

The term "(a,b)-leaper" (sometimes explicitly called a "single-pattern leaper") describes a fairy chess piece such as a knight that may make moves which simultaneously change ...

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 process of successively crossing out members of a list according to a set of rules such that only some remain. The best known sieve is the sieve of Eratosthenes for ...