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A Hamiltonian path, also called a Hamilton path, is a graph path between two vertices of a graph that visits each vertex exactly once. If a Hamiltonian path exists whose ...

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 digit sum s_b(n) is a sum of the base-b digits of n, which can be implemented in the Wolfram Language as DigitSum[n_, b_:10] := Total[IntegerDigits[n, b]]The following ...

It is possible to perform multiplication of large numbers in (many) fewer operations than the usual brute-force technique of "long multiplication." As discovered by Karatsuba ...

The integer sequence beginning with a single digit in which the next term is obtained by describing the previous term. Starting with 1, the sequence would be defined by "1, ...

The natural logarithm of 2 is a transcendental quantity that arises often in decay problems, especially when half-lives are being converted to decay constants. ln2 has ...

The word net has several meanings in mathematics. It refers to a plane diagram in which the polyhedron edges of a polyhedron are shown, a point set satisfying certain ...

As originally stated by Gould (1972), GCD{(n-1; k),(n; k-1),(n+1; k+1)} =GCD{(n-1; k-1),(n; k+1),(n+1; k)}, (1) where GCD is the greatest common divisor and (n; k) is a ...

The polynomials defined by B_(i,n)(t)=(n; i)t^i(1-t)^(n-i), (1) where (n; k) is a binomial coefficient. The Bernstein polynomials of degree n form a basis for the power ...

Cards are a set of n rectangular pieces of cardboard with markings on one side and a uniform pattern on the other. The collection of all cards is called a "deck," and a ...