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A plane partition is a two-dimensional array of integers n_(i,j) that are nonincreasing both from left to right and top to bottom and that add up to a given number n. In ...

A polygonal number is a type of figurate number that is a generalization of triangular, square, etc., to an n-gon for n an arbitrary positive integer. The above diagrams ...

An integer m such that if p|m, then p^2|m, is called a powerful number. There are an infinite number of powerful numbers, and the first few are 1, 4, 8, 9, 16, 25, 27, 32, ...

A prime link is a link that cannot be represented as a knot sum of other links. Doll and Hoste (1991) list polynomials for oriented links of nine or fewer crossings, and ...

The prime zeta function P(s)=sum_(p)1/(p^s), (1) where the sum is taken over primes is a generalization of the Riemann zeta function zeta(s)=sum_(k=1)^infty1/(k^s), (2) where ...

The branch of geometry dealing with the properties and invariants of geometric figures under projection. In older literature, projective geometry is sometimes called "higher ...

secz is the trigonometric function defined by secz = 1/(cosz) (1) = 2/(e^(iz)+e^(-iz)), (2) where cosz is the cosine. The secant is implemented in the Wolfram Language as ...

Separation of variables is a method of solving ordinary and partial differential equations. For an ordinary differential equation (dy)/(dx)=g(x)f(y), (1) where f(y)is nonzero ...

Given three noncollinear points, construct three tangent circles such that one is centered at each point and the circles are pairwise tangent to one another. Then there exist ...

A figurate number of the form P_n^((4))=1/6n(n+1)(2n+1), (1) corresponding to a configuration of points which form a square pyramid, is called a square pyramidal number (or ...